Question

Please help me with this math question!

Answer 1

1) Change radical forms to fractional exponents using the rule:
The nth root of "a number" = "that number" raised to the reciprocal of n.
For example $\sqrt[n]{3} = 3^{ \frac{1}{n} }$.

The square root of 3 ($\sqrt{3}$) = 3 to the one-half power ($3^{ \frac{1}{2} }$).
The 5th root of 3 ($\sqrt[5]{3}$) = 3 to the one-fifth power ($3^{ \frac{1}{5} }$).

2) Now use the product of powers exponent rule to simplify:
This rule says $a^{m} a^{n} = a^{m+n}$. When two expressions with the same base (a, in this example) are multiplied, you can add their exponents while keeping the same base.

You now have $(3^{ \frac{1}{2} })*(3^{ \frac{1}{5} })$. These two expressions have the same base, 3. That means you can add their exponents:
$(3^{ \frac{1}{2} })(3^{ \frac{1}{5} })\\ = 3^{(\frac{1}{2} + \frac{1}{5}) }\\ = 3^{\frac{7}{10}}$

3) You can leave it in the form $3^{\frac{7}{10}}$ or change it back into a radical $\sqrt[10]{3^7}$

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Answer: $3^{\frac{7}{10}}$ or $\sqrt[10]{3^7}$