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HELPP!!!!!!!!!!!!!!!!

HELPP!!!!!!!!!!!!!!!!-example-1

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Answer:

Explanation:

We'll take this step by step. The equation is


8-3\sqrt[5]{x^3}=-7

Looks like a hard mess to solve but it's actually quite simple, just do one thing at a time. First thing is to subtract 8 from both sides:


-3\sqrt[5]{x^3}=-15

The goal is to isolate the term with the x in it, so that means that the -3 has to go. Divide it away on both sides:


\sqrt[5]{x^3}=5

Let's rewrite that radical into exponential form:


x^{(3)/(5)}=5

If we are going to solve for x, we need to multiply both sides by the reciprocal of the power:


(x^{(3)/(5)})^{(5)/(3)}=5^{(5)/(3)}

On the left, multiplying the rational exponent by its reciprocal gets rid of the power completely. On the right, let's rewrite that back in radical form to solve it easier:


x=\sqrt[3]{5^5}

Let's group that radicad into groups of 3's now to make the simplifying easier:


x=\sqrt[3]{5^3*5^2} because the cubed root of 5 cubed is just 5, so we can pull it out, leaving us with:


x=5\sqrt[3]{5^2} which is the same as:


x=5\sqrt[3]{25}

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