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Maths-

General

Easy

Question

Simplify:
(64 / 125)^−2/3 ÷ (625 / 256)^1/4 × (−6)⁰

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 × ... × a n times.

The correct answer is: Simplifying the given expression, we get- 1.25 or 5/4.

Step-by-step solution:-
(64/125)^−2/3 ÷ (625/256)^1/4 × (−6)⁰
= (125/64)^2/3 ÷ (625/256)^1/4× 1 ….......................................... (b^-n = 1/bⁿ & b⁰ = 1)
= (5³/2⁶)^2/3 ÷ (5⁴/2⁸)^1/4
= 5³×^2/3 / 2⁶×^2/3 ÷ (5⁴×^1/4 / 2⁸×^1/4) …........................................... [(bⁿ)^m = b^nm]
= 5² / 2⁴ ÷ 5 / 2²
= 5² / 2⁴ × 2² / 5 ................................................................... (Taking reciprocal)
= 5² × 2² / 2⁴ × 5
= 5^2-1 / 2^4-2 ..................................................................................... (aⁿ/a^m = a^n-m)
= 5/2²
= 5/4
= 1.25
Final Answer:-
∴ Simplifying the given expression, we get- 1.25 or 5/4.

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