Question

Which expression is equivalent to (5x^3)(2x)^3

Answer 1

For this case we have the following expression:

$5x ^ 3 * (2x) ^ 3$

Rewriting we have:

$5x ^ 3 * (2x * 2x * 2x) =\\5x ^ 3 * 8x ^ 3 =$

For properties of multiplication of power of the same base we have that:

$a ^ m * a ^ n = a ^ {m + n}$

So:

$5x ^ 3 *8x ^ 3 = 40x ^ 6$

Answer:

$40x ^ 6$

Answer 2

Answer:

$\large\boxed{(5x^3)(2x)^3=40x^6}$

Step-by-step explanation:

$(5x^3)(2x)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\(5x^3)(2^3x^3)=(5x^3)(8x^3)\qquad\text{use commutative law}\\\\=(5\cdot8)(x^3x^3)\qquad\text{use}\ a^na^m=a^{n+m}\\\\=40x^{3+3}=40x^6$