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S_A_V [24]
3 years ago
5

Which expression is equivalent to (x4/3x2/3)1/3

Mathematics
1 answer:
Zolol [24]3 years ago
6 0

Given

The expression is given in the question

=(x^{\frac{4}{3}}\times\ x^{\frac{2}{3}})\ ^{\frac{1}{3}}

Find the expression is equivalent to the above expression.

To proof

As expression is given in the question

=(x^{\frac{4}{3}}\times\ x^{\frac{2}{3}})\ ^{\frac{1}{3}}

By using the properties

product of powers property tells us that when you multiply powers with the same base you just have to add the exponents.

i.e

x^{a} .x^{b} = x^{a +b}

Now using this in above

we get

=x^{\frac{6}{3}\times\frac{1}{3}}

Also by using the property

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

We get=x^{\frac{6}{9}}

Therefore expression becomes

= x^{\frac{2}{3}}

Hence proved








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