Question

simplify [(1/3)^-³–(1/2)^-3]÷(1/4)^-³

Answer 1

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Answer 2

Given,

An expression: [(1/3)^-³–(1/2)^-3]÷(1/4)^-³

To find,

The simplified value of the given expression.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If a, b, and x are three numbers, then, there exists an identity such that,

(a/b)^(-x) = (b/a)^(x) = {(b)^x}/{(a)^x}{Statement-1}

Now, according to the question;

On simplifying the given expression, we get,

[(1/3)^-³–(1/2)^-3]÷(1/4)^-³

= [(3/1)^³–(2/1)^³]÷(4/1)^³

{according to statement-1}

= [(3)^³–(2)^³]÷(4)^³

= [27–8]÷(4)^³

= (19)÷(64)

= 19/64

Hence, the simplified value of the given expression is equal to 19/64.