Question

9-47) if x to power (5y) = 2a wherea isnt 0, then x to power (30y) must equal which

a) 12a
b) 2a to power (6)
c) 64 a to power (6)

Answer 1

(c) 64 a to power (6)

Explanation:

We will use the following property:

`\displaystyle (a^b)^c = a^(bc)`

We are given:

`\displaystyle x^(5y) = 2a`
and we need to find the value of
`\displaystlye x^(30y)`

Notice that the power of x in the second expression is 6 times the power of x in the given equation.
If we raise the given equation by a power of 6, we will get the expected power of x. (using the property mentioned)

raising the given equation by a power of 6:

`\displaystyle (x^(5y))^6 = (2a)^6`

`\displaystyle x^(30y) = 64a^6`
Hence the correct answer is (c) 64 a to power (6)