Answer:
A) [tex] \dfrac{a^{6}}{b^{15}} [/tex]
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.
[tex] \left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n} [/tex]
Raising a power to a power.
Rule: To raise a power to a power, multiply the powers.
[tex] (a^m)^n = a^{mn} [/tex]
Your problem:
[tex] \left(\dfrac{a^2}{b^5}\right)^3 [/tex]
We follow the first rule and raise the numerator and the denominator to the 3rd power.
[tex] \left(\dfrac{a^2}{b^5}\right)^3 = [/tex]
[tex] = \dfrac{(a^2)^3}{(b^5)^3} [/tex]
Now we follow the second rule for both the numerator and denominator, and raise a power to a power by multiplying exponents.
[tex] = \dfrac{a^{2 \times 3}}{b^{5 \times 3}} [/tex]
[tex] = \dfrac{a^{6}}{b^{15}} [/tex]
Answer: A) [tex] \dfrac{a^{6}}{b^{15}} [/tex]
