Answer :
Let's simplify the expression [tex]\((5x^3)(4x)^3\)[/tex] step-by-step to find an equivalent expression.
1. Expression Breakdown:
- We have two parts of the expression: [tex]\(5x^3\)[/tex] and [tex]\((4x)^3\)[/tex].
2. Simplifying [tex]\((4x)^3\)[/tex]:
- Raise the coefficient [tex]\(4\)[/tex] to the power of [tex]\(3\)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
- Raise [tex]\(x\)[/tex] to the power of [tex]\(3\)[/tex]:
[tex]\[
(x^1)^3 = x^{1 \times 3} = x^3
\][/tex]
- So, [tex]\((4x)^3 = 64x^3\)[/tex].
3. Combine with [tex]\(5x^3\)[/tex]:
- Combine the coefficients from [tex]\(5x^3\)[/tex] and [tex]\(64x^3\)[/tex]:
[tex]\[
5 \times 64 = 320
\][/tex]
- Combine the exponents of [tex]\(x^3\)[/tex] from both parts:
[tex]\[
x^{3+3} = x^6
\][/tex]
4. Final Expression:
- The final simplified expression is:
[tex]\[
320x^6
\][/tex]
Hence, the expression [tex]\((5x^3)(4x)^3\)[/tex] is equivalent to [tex]\(320x^6\)[/tex]. The correct answer is [tex]\(320x^6\)[/tex].
1. Expression Breakdown:
- We have two parts of the expression: [tex]\(5x^3\)[/tex] and [tex]\((4x)^3\)[/tex].
2. Simplifying [tex]\((4x)^3\)[/tex]:
- Raise the coefficient [tex]\(4\)[/tex] to the power of [tex]\(3\)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
- Raise [tex]\(x\)[/tex] to the power of [tex]\(3\)[/tex]:
[tex]\[
(x^1)^3 = x^{1 \times 3} = x^3
\][/tex]
- So, [tex]\((4x)^3 = 64x^3\)[/tex].
3. Combine with [tex]\(5x^3\)[/tex]:
- Combine the coefficients from [tex]\(5x^3\)[/tex] and [tex]\(64x^3\)[/tex]:
[tex]\[
5 \times 64 = 320
\][/tex]
- Combine the exponents of [tex]\(x^3\)[/tex] from both parts:
[tex]\[
x^{3+3} = x^6
\][/tex]
4. Final Expression:
- The final simplified expression is:
[tex]\[
320x^6
\][/tex]
Hence, the expression [tex]\((5x^3)(4x)^3\)[/tex] is equivalent to [tex]\(320x^6\)[/tex]. The correct answer is [tex]\(320x^6\)[/tex].
