Question

Find the product.
(-5a ^2)^3 · a ^5

A. -15a^10
B. -125a^11
C. 15a^6
D.-125a^10

Answer 1

Answer:

Option B. -125a^11

Step-by-step explanation:

$(-5a^2)^{3}a^5=(-5)^3(a^2)^3a^5\\ (-5a^2)^{3}a^5=-125a^{2(3) }a^5\\(-5a^2)^{3}a^5=-125a^{6}a^5\\(-5a^2)^{3}a^5=-125a^{6+5}\\(-5a^2)^{3}a^5=-125a^{11}$

Answer 2

Answer: D. -125a^11

Step-by-step explanation:

1. You have the following expression:

$(-5a^{2})^{3}*a^{5}$

2. You must apply the exponent rule (Powers to powers): to raise a power to a power you must multiply the exponents:

 $(-125a^{6})(a^{5})$

3.  By the Product property of exponents, you can add the exponents when you mutiply two powers with equal base:

 $-125a^11$