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Maths-

General

Easy

Question

Simplify: [[1/4]⁴ × [1/4]⁴] ×[[3/⁵]¹² ÷ [3/5]⁵]

hint 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 × ... x a n times.

The correct answer is: Simplifying the given expression, we get the answer:- 37 / 216 × 57 = 2,187 / 5,12,00,00,000 = 0.00000043.

Step-by-step solution:-
[[1/4]⁴ × [1/4]⁴] ×[[3/5]¹² ÷ [3/5]⁵]
= [[1/2²]⁴]² × [[3/5]¹² ÷ [3/5]⁵] ….......................................... (m×m = m²)
= [1/2]¹⁶ × [[3/5]¹² ÷ [3/5]⁵] ….............................................. [(bⁿ)m = b^nm]
= [1⁸/2¹⁶] × [3¹²/5¹²] ÷ [3⁵/5⁵] ............................................. [aⁿ/bⁿ = (a/b)ⁿ]
= [1/2¹⁶] × [3¹²/5¹²] × [5⁵/3⁵] .............................................. (Taking reciprocal & 1ⁿ = 1)
= [1/2¹⁶] × [3¹² ×5⁵ / 5¹² × 3⁵]
= [1/2¹⁶] × [3^12-5 × 5^5-12] ...................................................... (aⁿ / a^m = a^n-m)
= [1/2¹⁶] × [3⁷× 5^-7]
= [1/2^16] × [3⁷ / 5⁷] ............................................................. (b^-n = 1 / bⁿ)
= 3⁷ / 2¹⁶ × 5⁷
∴ Simplifying the given expression, we get the answer:- 3⁷ / 2¹⁶ × 5⁷ = 2,187 / 5,12,00,00,000 = 0.00000043.

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