Question

Which expression is equivalent to (3^4 • 5^4)^-3

A. 1/15^3
B. 15^-48
C. 1/15^12
D. 15^5

Tania chose B as the correct answer, How did she get that?

Answer 1

3^4*5^4 = (3*5)^4 = 15^4

Raise this to the exponent -3 and we get

(3^4*5^4)^(-3) = (15^4)^(-3) = 15^(4*(-3)) = 15^(-12)

The last step is to use the rule

x^(-k) = 1/( x^k )

So,

15^(-12) = 1/( 15^12 )

The answer is actually choice C

It seems like Tania multiplied all the exponents to get 4*4*(-3) = 16*(-3) = -48, but you only multiply the inner and outer exponents together as I did when I went from (15^4)^(-3) to 15^(-12)