Question
The simplified expression for (3m2n9p9)2 is equivalent to 9m4n18p18 Hint: (1 point) Responses True True False False Skip to navigation page 2 of 3
Answers
GPT-4o mini
To simplify the expression \((3m^2n^9p^9)^2\), we need to apply the power of a product rule and the power of a power rule in exponents.
1. The expression can be expanded using the power of a product:
\((a \cdot b \cdot c)^n = a^n \cdot b^n \cdot c^n\).
2. Therefore:
\[
(3m^2n^9p^9)^2 = 3^2 \cdot (m^2)^2 \cdot (n^9)^2 \cdot (p^9)^2
\]
3. Now we compute each part:
- \(3^2 = 9\)
- \((m^2)^2 = m^{2 \cdot 2} = m^4\)
- \((n^9)^2 = n^{9 \cdot 2} = n^{18}\)
- \((p^9)^2 = p^{9 \cdot 2} = p^{18}\)
4. Putting it all together:
\[
(3m^2n^9p^9)^2 = 9m^4n^{18}p^{18}
\]
Thus, the original expression simplifies correctly to \(9m^4n^{18}p^{18}\).
The statement in the question is **True**.
1. The expression can be expanded using the power of a product:
\((a \cdot b \cdot c)^n = a^n \cdot b^n \cdot c^n\).
2. Therefore:
\[
(3m^2n^9p^9)^2 = 3^2 \cdot (m^2)^2 \cdot (n^9)^2 \cdot (p^9)^2
\]
3. Now we compute each part:
- \(3^2 = 9\)
- \((m^2)^2 = m^{2 \cdot 2} = m^4\)
- \((n^9)^2 = n^{9 \cdot 2} = n^{18}\)
- \((p^9)^2 = p^{9 \cdot 2} = p^{18}\)
4. Putting it all together:
\[
(3m^2n^9p^9)^2 = 9m^4n^{18}p^{18}
\]
Thus, the original expression simplifies correctly to \(9m^4n^{18}p^{18}\).
The statement in the question is **True**.