Question

Analyzing a Product of Powers to Find an Exponent
Determine the value of the variable in the product of powers.

What is the value of x in the product of powers 55 · 5x = 52 ?
x =
What is the value of y in the product of p-3 · p-6 = py
y =
What is the value of n in th product of 92 · 9-7 · 9n = 9-5 = StartFraction 1 Over 9 Superscript 5 EndFraction?
n =

Answer 1

Use a^m · a^n = a^{m+n}.

1) 5^5 · 5^x = 5^2 → 5 + x = 2 → x = -3.

2) p^{-3} · p^{-6} = p^y → -3 + (-6) = y → y = -9.

3) 9^2 · 9^{-7} · 9^n = 9^{-5} → 2 + (-7) + n = -5 → n = 0.