Question

If 5^n x 5^3 = 5^6, then n is _____.

A) 18
B) 2
C) 3
D) 9

Answer 1

n = 3

Explanation:

Using the rule of exponents

`a^(m)` ×
`a^(n)` ⇔
`a^((m+n))`

Given

`5^(n)` × 5³ =
`5^(6)` , then

`5^(n+3)` =
`5^(6)`

Since the bases on both sides are 5, the equate the exponents

n + 3 = 6 ( subtract 3 from both sides )

n = 3

Answer 2

Answer: C) 3

The rule we'll use is a^b*a^c = a^(b+c). So we add the exponents.

That means 5^n*5^3 = 5^(n+3)

So 5^n*5^3 = 5^6 turns into 5^(n+3) = 5^6

The bases are equal to 5, so the exponents be equal to one another.

n+3 = 6

n+3-3 = 6-3

n = 3

So 5^3*5^3 = 5^(3+3) = 5^6.