Respuesta :

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:

n = 3

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Given

[tex]5^{n}[/tex] × 5³ = [tex]5^{6}[/tex] , then

[tex]5^{n+3}[/tex] = [tex]5^{6}[/tex]

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

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

n = 3

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