Question

Choose the correct simplification of the expression the quantity:

Answer 1

The answer is letter A

Answer 2

Answer:

A) $\dfrac{a^{6}}{b^{15}}$

Step-by-step explanation:

Fraction raised to an exponent.

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

$\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}$

Raising a power to a power.

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

$(a^m)^n = a^{mn}$

Your problem:

$\left(\dfrac{a^2}{b^5}\right)^3$

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

$\left(\dfrac{a^2}{b^5}\right)^3 =$

$= \dfrac{(a^2)^3}{(b^5)^3}$

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

$= \dfrac{a^{2 \times 3}}{b^{5 \times 3}}$

$= \dfrac{a^{6}}{b^{15}}$

Answer: A) $\dfrac{a^{6}}{b^{15}}$