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Choose given statement is true or false:

Rakesh has solved some problem of exponents in the following ways:

${(x^{2})}^{3} = x^{2^{3}} = x⁸$

Tick on the correct option for the given solution.

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True

False

answer is B.

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Detailed Solution

The given statement is false.
Concept: First we will expand the given equation by using the exponent power rules .
Here , the equation solved by Rakesh is

{(x^{2})}^{3} = x^{2^{3}} = x^{8}

But, we are not satisfied with Rakesh's solution .
By theory of exponent, it is like

{(x^{a})}^{b} = x^{ab}

Therefore ,

{(x^{2})}^{3} = x^{2 \times 3}

= x^{6}

It proves that Rakesh's answer is wrong.
The right answer would be

= x^{6}

and not

= x^{8}

.
Hence the given statement is false.

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