How do you simplify $\sqrt[4]{{(3 x^{2})}^{4}}$ $root4((3x^2)^4)$ ?

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Answer 1 · 2016-05-25T13:49:43

Rewrite to get rid of the root sign to make it easier to work with and get to $3 x^{2}$ $3x^2$

Let's first start with the original:

$\sqrt[4]{{(3 x^{2})}^{4}}$ $root(4)((3x^2)^4)$

Now let's rewrite this to get rid of the root sign (I find working with fractional exponents to be easier):

${({(3 x^{2})}^{4})}^{\frac{1}{4}}$ $((3x^2)^4)^(1/4)$

When we take things that have an exponent and take them to a power, the 2 exponents multiply together, like this:

${(3 x^{2})}^{4 \cdot (\frac{1}{4})}$ $(3x^2)^(4*(1/4))$

${(3 x^{2})}^{1}$ $(3x^2)^1$

$3 x^{2}$ $3x^2$

How do you simplify 4√(3x2)4root4((3x^2)^4)?