Question

If 5^n x 5^3 = 5^6, then n is _____. A) 18 B) 2 C) 3 D) 9

Answer 1

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.

Answer 2

Answer:

n = 3

Step-by-step 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