Maths-

General

Easy

Question

# Compute [(64)^{−1/6} × (216)^{−1/3} × (81)^{1/4} ] / [(512)^{−1/3} × (16)^{1/4} × (9)^{−1/2}]

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: Value after simplifying the given equation is 3.

### Step-by-step solution:-

[(64)^{−1/6} × (216)^{−1/3} × (81)^{1/4}] / [(512)^{−1/3} × (16)^{1/4} × (9)^{−1/2}]

= [(81)^{1/4} × (512)^{1/3} × (9)^{1/2}] / [(64)^{1/6} × (216)^{1/3} × (16)^{1/4}] ...................................... (b^{-n} = 1/b^{n})

= [(3^{4})^{1/4} × (8^{3})^{1/3} × (3^{2})^{1/2}] / [(2^{6})^{1/6} × (6^{3})^{1/3 }× (2^{4})^{1/4}]

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

= 3 × 8 × 3 / 2 × 6 × 2

= 72 / 24

= 3

Final Answer:-

∴ Value after simplifying the given equation is 3.

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