Maths-
General
Easy
Question
Evaluate-
i. {(1/3)-1 - (1/4)-1)}-1
ii. (5/8)-7 × (8/5)-4
Hint:
In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
an = a × a × ... × a n times.
The correct answer is: Answers to the given equations are:- -1 & 512 / 125 = 4.096 respectively.
Step-by-step solution:-
i. {(1/3)-1 - (1/4)-1)}-1
= 1 / {(3/1)1 - (4/1)1}1 …................................................. (b-n = 1 / bn)
= 1 / {3 - 4} .................................................................... (b1 = b)
= 1 / -1
= -1
ii. (5/8)-7 × (8/5)-4
= (8/5)7 × (5/8)4 ............................................................ (b-n = 1 / bn)
= 87 / 57 × 54 / 84 .......................................................... [an/bn = (a/b)n]
= 87 × 54 / 57 × 84
= 87-4 / 57-4 .................................................................... (an/am = an-m)
= 83 / 53
= 512 / 125
Final Answer:-
∴ Answers to the given equations are:- -1 & 512 / 125 = 4.096 respectively.
Related Questions to study
Maths-
Are the bread slices used for preparing the sandwich congruent? Explain why or why not?
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)
Are the bread slices used for preparing the sandwich congruent? Explain why or why not?
![](data:image/png;base64,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)
Maths-General
Maths-
Anu notices that has a prime factor of 3 in the denominator, so he thinks the fraction will converto a recurring decimal. However when she enters the calculator , she finds that = 0.6Can you explain anu’s mistake ?
Anu notices that has a prime factor of 3 in the denominator, so he thinks the fraction will converto a recurring decimal. However when she enters the calculator , she finds that = 0.6Can you explain anu’s mistake ?
Maths-General
Maths-
Simplify: [2/3]3 × [2/3]−2 [[1/2]−2]2 × 1/24
Simplify: [2/3]3 × [2/3]−2 [[1/2]−2]2 × 1/24
Maths-General
Maths-
Prove that AB ≅ DC
![](data:image/png;base64,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)
Prove that AB ≅ DC
![](data:image/png;base64,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)
Maths-General
Maths-
Convert the following fraction to decimal
d) 13/55
Convert the following fraction to decimal
d) 13/55
Maths-General
Maths-
Convert the following fraction to decimal
c) 11/9
Convert the following fraction to decimal
c) 11/9
Maths-General
Maths-
Convert the following fraction to decimal
b) 13/65
Convert the following fraction to decimal
b) 13/65
Maths-General
Maths-
Solve for the value of m of the following-
a. 7m = 343
b. 2m-3 = 1
Solve for the value of m of the following-
a. 7m = 343
b. 2m-3 = 1
Maths-General
Maths-
of an isosceles triangle ABC is acute in which AB = AC and BD
AC . Prove that
![B C squared equals 2 cross times A C cross times C D text . end text](data:image/png;base64,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)
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)
of an isosceles triangle ABC is acute in which AB = AC and BD
AC . Prove that
![B C squared equals 2 cross times A C cross times C D text . end text](data:image/png;base64,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)
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UrMpytW7fi8ccfR48ePXDu3DmDjStJEoYPH67sfzRt2jRcv379b6+5kytXrgC4+dyRue2fpI8GGSCdTod3330XWVlZcHV1xauvvgpbW1u1yzKYTp06wdra2igP/3l7eyMqKgparRa//fYb5s6de9v3+aenY26FKTExEZ9//jk0Gg1mzpyJpk2bGrwu1aj9IUwN69evp42NDWVZ5ksvvaR2OUYRHx9PAFy5cqXBxy4vL1emqz08PHj48GGWlpZy2bJlyiZejRo1YmRkJN98800+8MAD7NWrF+Pj41leXm7wetTU4B6oy87OxpAhQ/Dtt9/Cw8MDp0+fhpeXl9plGcWYMWMQHx+Ps2fP4t577zXYuMePH8fYsWNx6tQpAMBTTz2FDz/8EElJSSgrK4ONjQ1IorS0FDqdDh4eHggJCamfq9pVDrBJVVdXMzY2Vpm23rBhg9olGV1oaCg9PT0NMlZ6ejqnTp1KR0dHZX0cANra2nLTpk0GOYalaVABSk1NpYeHB2VZZt++fZmXl6d2SSbh7e3NTp061fn9ZWVl/Pjjj9mhQwdKkkRJkhgYGMgFCxYwICCAABgaGsr09HQDVm0ZGlSAnn76acqyTDc3N+7cuVPtckwmMzOTNjY2HDFiRK3fm5yczIiICOUzo729PcePH6+0vVq/fr0SqrffftvQpZu9BhOgL774gg4ODpRlmWPHjlW7HJNbt24dAXD58uU1en1WVhZjY2Pp6upKWZap0WjYs2dP7t+//7bX5ebmsk+fPpQkiW5ubg3u8e8GEaDs7GyGhYVRkiS2bNmSycnJapekiujoaFpZWfHChQt3fU1FRQU3btzIsLAw5bNiy5YtGRcXd9dHGXbv3k13d3dKksRBgwYZq3yz1CACNG/ePEqSRFmWuWjRIrXLUVVYWBg9PDzu+L0LFy5w+PDhtLe3pyzLtLKy4pAhQ3jx4sV/XSMYGRmpTF8nJCQYo3SzVO8DlJKSwsDAQEqSxA4dOrCsrEztklTn4+PDjh07Kn/Ozs7mokWL2LhxY+UXTZs2bfjll1/WeMyTJ0/Sz8+PANi9e3cWFRUZo3SzU68DVFFRwbFjxyqrgA8cOKB2SWYhKyuLtra2HDZsGHfs2MHu3btTo9FQkiR6enpy5syZvHbtWq3HvbXiWpIkxsXFGaFy81OvA3TkyBFqNBoC4PPPP1/v7oLrY/HixQRAGxsbSpJEjUbDvn378vjx49TpdHUas6ysTNl3tW3btvz5558NXLX5qbcBKikpYWhoKAHQ39+fKSkpapdkFnJycrh8+XJ6eXkpN0IDAwP50UcfGWT8zZs308rKigA4depUVlVVGWRcc1VvA7RkyRJKkkQAnD9/vtrlqK66upr79u1jeHg4raysKEkSXV1dOXnyZIPeAC0rK+OIESOUFQrHjh0z2NjmqF4G6MKFC2zVqhUlSWLHjh3522+/qV2SqvLy8jhhwgQ6Ozsrl2u9evXikSNHeOPGDYMf79ixY2zSpAkB8MknnzT4+OakXgYoKiqKkiTR0dGxQfcyKyoq4qeffqrMQkqSxHvvvZerVq0y6qPr1dXVfOONNwiAGo2G69evN9qx1FbvArRv3z56eHhQkiQ+8cQTapejmh9//JHPPfcc7e3tKUkSGzVqxJdeeolpaWkmOf6VK1cYEhJCAAwKCuLvv/9ukuOaWr0KUG5uLp988klKkkQXF5cGMQv0V4WFhYyJiVHadGm1WoaFhfHQoUMm74azZMkSarVaAuCMGTNMemxTqVcB+uyzz5RLlTlz5qhdjkmVlpZy8+bNDAkJUZbgtGjRgnFxcao1yC8vL2d4eDgB0M/Pj0ePHlWlDmOqNwG6du0aAwICKMsyQ0JC6l0Dv39y4cIFjhw5ks7OzpRlmTY2NhwzZoxZnIGPHDmiTGtHRkbWu5Ug9SZAEydOVGaYGsKDcuTNSYJ33nlHecZJq9UyKCiIu3fvNpttWXQ6HaOiogiAVlZWPHjwoNolGVS9CNCRI0eUdVwRERH1fh1WRUUFExIS2LlzZ+VyrUmTJnzzzTeZk5Ojdnl/c/78eTZr1owA2K1bNxYXF6tdksFYfIDKy8uViYN77rmHP/zwg9olGVVaWhqjoqLYuHFjJTwDBw7k4cOHzbqr6rvvvqusfHjvvffULsdgLD5AGzZsUKZq62uHHfLm0qQVK1awadOmyuVaQEAAN2zYYBGfK3777Td27tyZAOjr68uMjAy1SzIIiw7Q5cuX2alTJ0qSxICAgHq5p49Op+OePXvYo0cP5Yzj4uLC119/nZmZmWqXVyufffYZHRwcCIBjxoxRuxyDsOgALViwQJm2ro93u9PT0zlhwgRlkuBWM5SDBw9a7CLNp556Suknt3fvXrXL0ZvFBujHH3+kg4MDJUliv3796tVW9OXl5fzss8/YsmVLpR+Bv78/16xZw9LSUrXL08vJkyeVtlj1YcLHYgPUv39/pZHFd999p3Y5BpOYmMhBgwYpXXAcHBz40ksv8ddff1W7NIOZNWuW8uCdpd9ysMgAbdmyhba2tpQkidHR0RZ7OfNnf/zxB2fPnk0fHx/lcq1nz57cu3dvnR9wM1dZWVlKC+Dg4GCznHqvKYsLUG5uLtu1a0dJkhgcHMyLFy+qXZJeKisruWXLltuW4DRr1oxLly6tV/dL/upWmy0AFr3syuICFBMTozS+mDdvntrl6OX06dMcOXKk0gXHzs7ObJbgGFthYSGffvppAqCTkxN//PFHtUuqE4sK0MmTJ+nv709JkvjII49Y7JbrxcXFfPvtt9m8eXPlrBMaGsqEhASjPOBmrhISEujm5kYAFttPzmICVF5eznHjxik3ES1xTZVOp+POnTv58MMPK8Fxc3PjtGnTmJ+fr3Z5qhg5ciQB0MXFhVu2bFG7nFqzmADt2rWLjo6OlGWZ48ePt7jf1GfOnGF0dDQbNWqkhOeZZ57h4cOH1S5NVVevXqWvr6/STy4rK0vtkmrFIgJUUVHBjh07UpZl+vv7W9TEQVlZGZcsWaJcekqSxFatWvGTTz6x+Hs6hjJv3jxlQsEYG4IZk0UEaMmSJcpv7cWLF6tdTo1UV1fzm2++Ybdu3ZTgODs789VXX7W437LGVlJSoqyT8/f3t6hJFLMP0Pnz55V7I7169WJubq7aJf2rn3/+ma+88orSBUeSJP73v//lN998o3ZpZmvPnj20trYmAI4bN85i7u2ZfYBefPFFyrJMR0dHs79rXVlZyTVr1vC+++5TguPr68vVq1fX63s6hlBcXMxhw4YRAO3s7HjixAm1S6oRsw7Qtm3b6OLiQlmWOXjwYLN+3uXUqVOMiIhQguPo6Mjo6OgGuWtbXSUmJrJ58+YEwJ49e5q8CUpdmG2A8vPzOWDAAMqyTFdXV7OdOMjOzmZsbCy9vLyUTqiPPvpog9oBz5CmTJmiPP69bNkytcv5V2YboPfff1+ZOIiNjVW7nDvasWMHO3XqRFmWKUkSmzZtyiVLltSrleGmlpmZyXvvvZcALKKrrFkGKCMjgy1atKAsywwLC+P169fVLuk2ycnJHDVqFLVardK0cMSIESZrWljfffHFF8quGpMnT1a7nH9klgGaOHEiZVmmra0tN27cqHY5iry8PL7zzjv08/NTzo5du3Zt0O2DjeHGjRvs3bs3AdDT05OnTp1Su6S7MrsAHTx4kE5OTpRlmUOHDjWb9kz79+9nWFgYrayslC448+bNY0FBgdql1Us//PCDMq0dGRlpNj8Hf2VWAaqsrORjjz1GSZLo4+NjFg/KnTt3jmPHjlWCY21tzaeeeqreb9uhtqqqKk6fPl1ZobBjxw61S7ojswrQqlWraG1tTUmSOGXKFFVrKSoq4nvvvUd/f3/lci0oKIgffPCB2f42rG/OnDnD++67jwAYEhJiljsMmk2A0tLS+NBDDylb0au54uCHH35g9+7daW1tTVmW6ezszIkTJ4p7OipYtGiRcm/NHDdKM5sA3XpQTs0OOxcvXuT//d//KcGxtrbm448/bpGPTtQXRUVF7N69OwGwefPmZjehYBYB+umnn5R1Y/369TP5KuWysjKuWbOGgYGByuVay5YtuWLFCot9aK8+2bx5M21tbQmA48ePV7uc26geIJ1Op3TYcXBwMPnzMUlJSQwPD6etra3SBSc6OrpedcGpDwYPHqw8eGdOi3JVD9Ann3xCjUZDSZJMuglTZmYm58+fT1dXV8qyTCsrK/bq1Yu7d+82WQ1CzV2+fFl5/Ds8PJx5eXlql0RS5QDl5+ezQ4cOlCSJrVu35rlz54x+zKqqKm7bto1hYWHUarWUZZk+Pj5cvHgx//jjD6MfX6i7uXPnKtPa5nKDXdUATZ48mZIk0dramkuXLjX68S5cuMARI0YoXXAaNWrE4cOH89KlS2a90lu4KSMjg4888ojSoN4c9l1VLUBHjx5l8+bNlQ47xuxxcP36dcbFxdHT01Npldu1a1du27bNaMcUjGP9+vXKCgVz2I1DlQCVlJRw1KhRlCSJtra2Rp04uLWzwa1WuR4eHpw7d65FPNkq/F1xcTH79OlDAPTy8uLJkydVrUeVAH399dfKPZ+XX37ZKJdPaWlpjI6OpoODg7IwtW/fvvz555/F5ZqFO3z4MJs0aUIA7Nevn6orFEweoPz8fHbt2lW513Lp0iWDj798+XL6+vr+bQmOpbXCEu7uxRdfJADa2Njw008/Va0Okwdo4cKFyg/2ihUrDDr2d999x0cffVS5p2NnZ8dJkyY1qB27G4r09HS6u7sTAB977DHVNlczaYAuXbqkfJDv1auXwdo7Xblyha+88gobNWpESZJoY2PDXr168ejRoxbT3UWovfj4eGVaW611ciYN0KBBgyjLMhs3bszt27frPV5xcTHXrl3LVq1a3da0cPny5aJpYQOQm5vL8PBwZcc7NZ4INlmAduzYQXd3d8qyzCFDhug93vHjx/n4448rZx2NRsNx48aJx6obmC1bttDGxkbpJ2dqJglQVlYWe/fuTVmW6eXlxZSUlDqPlZ+fzxkzZtDR0VG5CdulSxceOHBAXK41UJGRkQRAe3t7k9/bM0mAVq5cqUwc1LVVUWVlJTdv3qzsyi1JEv38/Lho0SLxWHUDl5SUxGbNmin95Ex5+W70AF2+fJkBAQGUZZkhISF1uoF56dIlDhs2jC4uLkp4Ro0aZba94gTTmzZtmtJPzpQN6o0eoDFjxig3Mnft2lWr9xYWFvLdd99lkyZNKEkStVotH374Ye7atUvcDBVuU1xczNatWxMAW7duzfPnz5vkuEYNUGJiorIfzogRI2p8aq2qqmJCQgK7d++uNC308vLinDlzVJvvF8zfpk2blGnt2bNnm+SXrNECVF5ezp49e1KWZbZo0YKJiYk1et/Vq1cZFRVFNzc35XPTs88+a5JHHQTLVlJSwv79+xMA3d3dmZSUZPRjGi1AK1asUBZw1qTDTklJCVetWkVvb29lxXRgYCA///xzMbsm1NiJEyeUB++eeOIJo//sGCVAFy9eZPv27SlJEkNCQv71uY29e/cyPDxcecDN0dGRkyZN4uXLl41RnlDPTZw4kQCo1WoNcsP+nxg8QNXV1ZwyZYoyW/bll1/e9bUZGRl8+eWXlRussiwzPDychw4dEpMEQp1dvHiRbdq0IQC2a9eOmZmZRjuWwQN07NgxZdasX79+d9zjpby8nOvWrVMayMuyzICAAK5cuVI0LRQMYunSpdRqtQRg1F4bBg1QeXk5w8PDKUkS3d3d77jL2Hfffccnn3xS6b1mb2/PCRMmWNS+mIL5Ky4uZqdOnQiA9913H5OTk41yHIMG6Msvv1Qu3aZPn37b97Kzs/n666/Tw8NDOet069aN+/btE5MEglF8//33lGWZAPjCCy8YZYWCwQKUmZnJFi1aUJIkdurUiampqSRv9n3bvn0727ZtS0mSlK3qFy1aJJoWCkZVVVWlPHin0Wj47bffGvwYBgvQnzvs3FpKkZyczNGjRysrpq2srMHjEloAAARASURBVBgZGanXYlJBqI2zZ8/Sx8eHANirVy+Db/ZskAAdPnyYzZo1oyRJ7N27N69fv87FixfT19dXuaR78MEH+dVXX1Gn0xnikIJQY3FxccoKhSVLlhh0bL0DVFpayiFDhlCSJLq6ujImJobdu3e/bcV0bGysWDEtqCYjI4NdunQhAPr5+Rl0lw29A7Rt2zba2NgoAWrcuLHygNuQIUNMspxCEP5NfHw87ezsCICvvPKKwcbVK0C5ublKa94/f4WGhnLPnj1idk0wK7ca1Ht4eHDv3r0GGVMLPaxcuRJJSUm3/Z2vry8iIiJQXl6OrVu3oqqq6q7vlyTpX49BUp8SBQEAYGVlhWbNmkGr1SI7Oxvx8fEICwuDvb29fgPXNXnJycl0cnJSPpzV9OvPZ6pb94P+6UuSpFofQ3yJr3/70mg0/Oijj9Q7A33wwQewt7eHs7Nzrd7357NOTc9A4iwkGFpFRQV27NiB/v37w9HRsc7jSBQ/nYJQZ7IhBhEZFCyNoX5ma30Jd/HiRcyePRuJiYmorKyEg4MDvL29UVBQgOzsbAwfPhzR0dHw9vY2SIGCYAilpaXYvXs3tm7dipSUFDg7OyM4OBjt27dHYGAgqqur0aVLl9oPXNcPT7179yZw86k/kjx37pzS1GHw4MEsKyvT+wOaIBhCRkYGBw0aRAAcOnSostP3jRs3GB8fzzZt2tR5Z/g6TyI4OTnd9ufAwEB07doVKSkp+PXXX5GTkwMfH5+6Di8IBlFZWYkFCxZg48aN6Nu3L9auXQsbGxsAgFarxciRI9GyZUvk5OTUafw6B4j/u4b8448/cOnSJezatQsbN25E69atERMTI8IjmIWUlBSsWLECABAREaGE58/CwsKg0+nqNL5eN1IB4OrVq4iLi0NGRgasrKzQsWNHuLm56TusIBjE6dOnlXDc7ZaLRqOBRqOp0/h6z8K1adMGy5cvx6ZNmxAVFYV169Zh2LBhOHfunL5DC4LePD09lf8uKysz+Ph1DtBfb4JaWVkhLCwMAHD27FmcPXtWv8oEwQAeeOABtGnTBgCwf//+O16qlZSUoLCwsE7j1zlAlZWVt/352rVr2LBhAwAgODgYwcHBdR1aEAzG19cXsbGx8PT0RHx8PNatW4eioiIAgE6nw759+7Bs2TLk5eXVafxar0RITU3FggULsHnzZuTl5cHT0xOhoaFIT0/HmTNnMGrUKAwfPhwPP/xwnQoSBGM4d+4cVq9ejW+++Qaurq5wcXHBPffcAz8/P/Tt2xft2rWr07i1DtCNGzeQl5cHjUYDrVYLnU6HiooKaDQaWFtbw8XFBbJskAUOgmBQJFFUVISSkhJUVVXBxsYGzs7OsLa2rvOYYi2cIOhBnCoEQQ8iQIKgBxEgQdCDCJAg6EEESBD0IAIkCHoQARIEPYgACYIeRIAEQQ8iQIKgBxEgQdDD/wM5gQ6FVc3UGwAAAABJRU5ErkJggg==)
Maths-General
Maths-
Convert the following fraction to decimal
a) 9/11
Convert the following fraction to decimal
a) 9/11
Maths-General
Maths-
Express the following recurring decimals as vulgar fraction
b) 0.743434343......
Express the following recurring decimals as vulgar fraction
b) 0.743434343......
Maths-General
Maths-
ABC is a triangle in which AB = AC. P is any point in its interior such
that
. Prove that AP bisects ![straight angle BAC](data:image/png;base64,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)
![](data:image/png;base64,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)
ABC is a triangle in which AB = AC. P is any point in its interior such
that
. Prove that AP bisects ![straight angle BAC](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
Evaluate:
a−3b−4 / a−2b−3
Evaluate:
a−3b−4 / a−2b−3
Maths-General
Maths-
Prove that ∠BAC ≅ ∠CAD
![](data:image/png;base64,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)
Prove that ∠BAC ≅ ∠CAD
![](data:image/png;base64,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)
Maths-General
Maths-
Express the following recurring decimals as vulgar fraction
a) 0.444444444
Express the following recurring decimals as vulgar fraction
a) 0.444444444
Maths-General