Answer:
B. 3¹²
Step-by-step explanation:
To solve this we need to apply the following laws of exponents:
1. [tex](a^n)^m=a^{n*m}[/tex]
2. [tex]a^{-n}=\frac{1}{a^n}[/tex]
Let's apply the first law to the numerator of our fraction and the second law to the denominator. For the numerator, [tex](3^5)^2[/tex], [tex]a=3[/tex], [tex]n=5[/tex], and [tex]m=2[/tex]. For the denominator [tex]3^{-2}[/tex], [tex]a=3[/tex] and [tex]n=-2[/tex]
Replacing values
[tex]\frac{(3^5)^2}{3^{-2}} =\frac{3^{5*2}}{\frac{1}{3^2} } =\frac{3^{10}}{\frac{1}{3^2} }[/tex]
Now, remember that to divide fractions we just need to invert the order of the second fraction and multiply:
[tex]\frac{3^{10}}{\frac{1}{3^2} }=3^{10}*\frac{3^2}{1} =3^{10}*3^2[/tex]
Finally, we can use the law of exponents for multiplication to get our answer:
[tex]a^n*a^m=a^{n+m}[/tex]
[tex]3^{10}*3^2=3^{10+2}=3^{12}[/tex]
We can conclude that the correct answer is B. 3¹²
