Maths-

General

Easy

Question

# Simplify:

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

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/b^{n} & b^{0} = 1)

= (5^{3}/2^{6})^{2/3} ÷ (5^{4}/2^{8})^{1/4}

= 5^{3}×^{2/3} / 2^{6}×^{2/3} ÷ (5^{4}×^{1/4} / 2^{8}×^{1/4}) …........................................... [(b^{n})^{m} = b^{nm}]

= 5^{2} / 2^{4} ÷ 5 / 2^{2}

= 5^{2} / 2^{4} × 2^{2} / 5 ................................................................... (Taking reciprocal)

= 5^{2} × 2^{2} / 2^{4} × 5

= 5^{2-1} / 2^{4-2} ..................................................................................... (a^{n}/a^{m} = a^{n-m})

= 5/2^{2}

= 5/4

= 1.25

Final Answer:-

∴ Simplifying the given expression, we get- 1.25 or 5/4.

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