Respuesta :

Answer:

Step-by-step explanation:

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

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

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:

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

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:

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

Let's rewrite that radical into exponential form:

[tex]x^{\frac{3}{5}}=5[/tex]

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

[tex](x^{\frac{3}{5}})^{\frac{5}{3}}=5^{\frac{5}{3}}[/tex]

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:

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

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

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

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

[tex]x=5\sqrt[3]{25}[/tex]

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