Question

Simplify the expression start fraction 2 a left parenthesis a squared b right parenthesis cubed over a superscript 4 baseline b superscript 5 baseline end fraction.
(1 point)
Responses

start fraction 2 a cubed over b squared end fraction
Image with alt text: start fraction 2 a cubed over b squared end fraction

start fraction 2 a squared over b squared end fraction
Image with alt text: start fraction 2 a squared over b squared end fraction

start fraction 8 a squared over b end fraction
Image with alt text: start fraction 8 a squared over b end fraction

start fraction 8 a cubed over b end fraction

Answer 1

To simplify the expression \(\frac{2a (a^2b)^3}{a^4b^5}\), we start by simplifying the numerator.

1. **Calculate \((a^2b)^3\)**:
\[
(a^2b)^3 = a^{2 \cdot 3} b^{1 \cdot 3} = a^6b^3
\]

2. **Multiply by \(2a\)**:
\[
2a(a^6b^3) = 2a^1 a^6 b^3 = 2a^{1+6}b^3 = 2a^7b^3
\]

Now, we rewrite the expression using this result:
\[
\frac{2a^7b^3}{a^4b^5}
\]

3. **Simplify the fraction**:
- For the \(a\) terms:
\[
\frac{a^7}{a^4} = a^{7-4} = a^3
\]
- For the \(b\) terms:
\[
\frac{b^3}{b^5} = b^{3-5} = b^{-2}
\]

Putting it all together, we get:
\[
\frac{2a^3}{b^2}
\]

Thus, the simplified expression is:
\[
\frac{2a^3}{b^2}
\]

The correct answer is:
\[
\frac{2a^3}{b^2}
\]