1 Answer

Mmiika · Answer 1 · 2021-08-30T06:27:07+0000

$x^2\left(\sqrt[4]{x^2}\right)$

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Step-by-step explanation:

The fourth root of x is the same as x^(1/4)

I.e,

$\sqrt[4]{x} = x^(1/4)$

The same applies to x^10 as well

$\sqrt[4]{x^(10)} = \left(x^(10)\right)^(1/4)$

Multiply the exponents 10 and 1/4 to get 10/4

$\sqrt[4]{x^(10)} = \left(x^(10)\right)^(1/4) = x^(10*1/4) = x^(10/4)$

$\sqrt[4]{x^(10)} = x^(10/4)$

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If we have an expression in the form x^(m/n), with m > n, then we can simplify it into an equivalent form as shown below

$x^(m/n) = x^a\sqrt[n]{x^b}$

The 'a' and 'b' are found through dividing m/n

m/n = a remainder b

'a' is the quotient, b is the remainder

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The general formula can easily be confusing, so let's replace m and n with the proper numbers. In this case, m = 10 and n = 4

m/n = 10/4 = 2 remainder 2

We have a = 2 and b = 2

So

$x^(m/n) = x^a\sqrt[n]{x^b}$

turns into

$x^(10/4) = x^2\sqrt[4]{x^2}$

which means

$\sqrt[4]{x^(10)} = {x^2} \sqrt[4]{x^2}$

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