Question

What is the simplified form of (a5^/b^3)^2
?(1 point)
Responses

a10b6
the fraction with numerator A to the 10th power and denominator b to the 6th power

a7b5
the fraction with numerator A to the 7th power and denominator b to the 5th power

a5b6
the fraction with numerator A to the 5th power and denominator b to the 6th power

a10b5

Answer 1

To simplify the expression \((\frac{a^5}{b^3})^2\), we apply the exponent to both the numerator and the denominator separately:

\[
(\frac{a^5}{b^3})^2 = \frac{(a^5)^2}{(b^3)^2}
\]

Now simplify each part:

- \((a^5)^2 = a^{5 \cdot 2} = a^{10}\)
- \((b^3)^2 = b^{3 \cdot 2} = b^{6}\)

Putting it all together, we get:

\[
\frac{a^{10}}{b^6}
\]

So, the simplified form of \((\frac{a^5}{b^3})^2\) is \(\frac{a^{10}}{b^{6}}\).

Among the responses provided, the correct answer is:

**the fraction with numerator A to the 10th power and denominator b to the 6th power**.