Question

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)`

Answer 1

The answer is letter A

Answer 2

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))`