Question

The simplified expression for (3m2n9p9)2
is equivalent to 9m4n18p18

Hint:



(1 point)
Responses

True
True

False

Answer 1

To simplify the expression \((3m^2n^9p^9)^2\), we apply the power of a product property, which states that \((ab)^n = a^n \cdot b^n\).

So we can break it down as follows:

\[
(3m^2n^9p^9)^2 = 3^2 \cdot (m^2)^2 \cdot (n^9)^2 \cdot (p^9)^2
\]

Calculating each part:

- \(3^2 = 9\)
- \((m^2)^2 = m^{2 \cdot 2} = m^4\)
- \((n^9)^2 = n^{9 \cdot 2} = n^{18}\)
- \((p^9)^2 = p^{9 \cdot 2} = p^{18}\)

Now, combining these results gives:

\[
9m^4n^{18}p^{18}
\]

Thus, the simplified expression \((3m^2n^9p^9)^2\) is indeed equivalent to \(9m^4n^{18}p^{18}\).

Therefore, the statement is **True**.