Choose the correct simplification of the expression the quantity: (a^(2) )/(b^(5))^(3) A) (a^(6))/(b^(15)) B) (a^(5))/(b^(8)) C) (a)/(b^(15) ) D) ax^(6)bx^(15)

Question

asked Nov 26, 2020 71.8k views

2 Answers

Mohsen Heydari · Answer 1 · 2020-12-02T05:59:48+0000

Answer:

A)
(a^(6))/(b^(15))

Explanation:

Fraction raised to an exponent.

Rule: To raise a fraction to an exponent, raise the numerator and the denominator to the exponent.

$\left((a)/(b)\right)^n = (a^n)/(b^n)$

Raising a power to a power.

Rule: To raise a power to a power, multiply the powers.

(a^m)^n = a^(mn)

Your problem:

$\left((a^2)/(b^5)\right)^3$

We follow the first rule and raise the numerator and the denominator to the 3rd power.

$\left((a^2)/(b^5)\right)^3 =$

= ((a^2)^3)/((b^5)^3)

Now we follow the second rule for both the numerator and denominator, and raise a power to a power by multiplying exponents.

= (a^(2 * 3))/(b^(5 * 3))

= (a^(6))/(b^(15))

Answer: A)
(a^(6))/(b^(15))