Certainly! Let's simplify the expression [tex]\((4a)^3\)[/tex] step-by-step.
1. Identify the base and the exponent:
- In the expression [tex]\((4a)^3\)[/tex], the base is [tex]\(4a\)[/tex] and the exponent is 3. This means we need to multiply [tex]\(4a\)[/tex] by itself three times.
2. Expand the expression:
- [tex]\((4a)^3\)[/tex] can be written as:
[tex]\[
(4a) \times (4a) \times (4a)
\][/tex]
3. Distribute the exponent to each factor inside the parenthesis:
- We apply the exponent separately to the constant and the variable:
[tex]\[
(4a) \times (4a) \times (4a) = 4 \times 4 \times 4 \times a \times a \times a
\][/tex]
4. Simplify the constants:
- Calculate [tex]\(4 \times 4 \times 4\)[/tex]:
[tex]\[
4 \times 4 = 16
\][/tex]
[tex]\[
16 \times 4 = 64
\][/tex]
- So, the constant part simplifies to 64.
5. Simplify the variables:
- For the variable [tex]\(a\)[/tex], we have [tex]\(a \times a \times a\)[/tex], which is [tex]\(a^3\)[/tex].
6. Combine the simplified constants and variables:
- Putting it all together, we have:
[tex]\[
64 \times a^3
\][/tex]
Therefore, the simplified form of [tex]\((4a)^3\)[/tex] is:
[tex]\[
64a^3
\][/tex]
So, the final answer is:
[tex]\[
64a^3
\][/tex]
