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Maths-

General

Easy

Question

Find the value of p so that
$left parenthesis 4 divided by 5 right parenthesis cubed divided by left parenthesis 4 divided by 5 right parenthesis to the power of negative 3 end exponent equals left parenthesis 4 divided by 5 right parenthesis to the power of 3 p end exponent$

hint Hint:

In Mathematics, lets say, "a" represents a number and " " 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.
$a to the power of n equals a cross times a cross times horizontal ellipsis cross times a$ n times.

The correct answer is: 2

Step-by-step solution:-
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell left parenthesis 4 divided by 5 right parenthesis cubed divided by left parenthesis 4 divided by 5 right parenthesis to the power of negative 3 end exponent equals left parenthesis 4 divided by 5 right parenthesis to the power of 3 p end exponent end cell row blank row blank row blank end table$
$table attributes columnalign right columnspacing 0em end attributes row cell therefore left parenthesis 4 divided by 5 right parenthesis to the power of 3 minus left parenthesis negative 3 right parenthesis end exponent equals left parenthesis 4 divided by 5 right parenthesis to the power of 3 p end exponent midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis open parentheses a to the power of n divided by a to the power of m equals a to the power of n minus m end exponent close parentheses end cell row blank row blank end table$
$table attributes columnalign right columnspacing 0em end attributes row cell therefore left parenthesis 4 divided by 5 right parenthesis to the power of 3 plus 3 end exponent equals left parenthesis 4 divided by 5 right parenthesis to the power of 3 p end exponent end cell row blank end table$
$therefore left parenthesis 4 divided by 5 right parenthesis to the power of 6 equals left parenthesis 4 divided by 5 right parenthesis to the power of 3 p end exponent$
$table attributes columnalign left center columnspacing 1em end attributes row therefore cell 6 equals 3 straight p horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis end cell row blank blank row blank blank end table$ (Exponents of the same base in an equation are equal)
$table attributes columnalign left center columnspacing 1em end attributes row therefore cell 6 divided by 3 equals straight p end cell row therefore cell 2 equals straight p end cell end table$
i.e. p=2
Final Answer:-
Value of p for the given equation is 2 .

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