Question

(3⁵)²/3⁻² A. 3¹⁰ B. 3¹² C. alt="3^{9}" align="absmiddle" class="latex-formula">

D. $3^{8}$

Answer 1

Answer:

B. 3¹²

Step-by-step explanation:

To solve this we need to apply the following laws of exponents:

1. $(a^n)^m=a^{n*m}$

2. $a^{-n}=\frac{1}{a^n}$

Let's apply the first law to the numerator of our fraction and the second law to the denominator. For the numerator, $(3^5)^2$, $a=3$, $n=5$, and $m=2$. For the denominator $3^{-2}$, $a=3$ and $n=-2$

Replacing values

$\frac{(3^5)^2}{3^{-2}} =\frac{3^{5*2}}{\frac{1}{3^2} } =\frac{3^{10}}{\frac{1}{3^2} }$

Now, remember that to divide fractions we just need to invert the order of the second fraction and multiply:

$\frac{3^{10}}{\frac{1}{3^2} }=3^{10}*\frac{3^2}{1} =3^{10}*3^2$

Finally, we can use the law of exponents for multiplication to get our answer:

$a^n*a^m=a^{n+m}$

$3^{10}*3^2=3^{10+2}=3^{12}$

We can conclude that the correct answer is B. 3¹²