Question
What is the simplified form of (5a2
b)3
?(1 point)
Responses
53
a5
b3
53a5b3
53
a6
b3
53a6b3
5a6
b3
5a6b3
53
a6
b
b)3
?(1 point)
Responses
53
a5
b3
53a5b3
53
a6
b3
53a6b3
5a6
b3
5a6b3
53
a6
b
Answers
GPT-4o mini
To simplify the expression \((5a^2b)^3\), we will apply the power of a product property.
1. Distribute the exponent to each factor inside the parentheses:
\[
(5a^2b)^3 = 5^3 \cdot (a^2)^3 \cdot b^3
\]
2. Calculate each part:
\[
5^3 = 125
\]
\[
(a^2)^3 = a^{2 \cdot 3} = a^6
\]
\[
b^3 = b^3
\]
3. Combining all parts together:
\[
(5a^2b)^3 = 125a^6b^3
\]
So, in simplified form, the answer is:
\[
125a^6b^3
\]
If you want to express \(125\) as \(5^3\), it can be written as:
\[
5^3a^6b^3
\]
Among the options provided, the correct simplified form is:
\[
5^3a^6b^3
\]
1. Distribute the exponent to each factor inside the parentheses:
\[
(5a^2b)^3 = 5^3 \cdot (a^2)^3 \cdot b^3
\]
2. Calculate each part:
\[
5^3 = 125
\]
\[
(a^2)^3 = a^{2 \cdot 3} = a^6
\]
\[
b^3 = b^3
\]
3. Combining all parts together:
\[
(5a^2b)^3 = 125a^6b^3
\]
So, in simplified form, the answer is:
\[
125a^6b^3
\]
If you want to express \(125\) as \(5^3\), it can be written as:
\[
5^3a^6b^3
\]
Among the options provided, the correct simplified form is:
\[
5^3a^6b^3
\]