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

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

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`