Answer:
It is the second answer [tex]3^{8} b^{10}[/tex]
Step-by-step explanation:
This is easier to understand if you write it out in expanded form.
[tex](3^{4} b^{5}) ^{2}[/tex] means
[tex](3^{4} b^{5})[/tex][tex](3^{4}b^{5)}[/tex] We do this twice because that is what the exponent tells us to do that is outside of the parentheses.
Now write this out in expanded form and we will have
(3x3x3x3xbxbxbxbxb)(3x3x3x3xbxbxbxbxb) If we put all of the 3's and b's together we get
3x3x3x3x3x3x3x3xbxbxbxbxbxbxbxbxbxb
[tex]3^{8} b^{10}[/tex]
the power of powers principle tells us that when we have an exponent raised to an exponent, we multiple the exponents. (4 x 2 = 8 and 5 x 2 = 10)