+2446 Your question appears to want one to evaluate the expression \(\sqrt{(108b)^4}\). Let me try to make it easier so that the calculator is not necessary:
| \(\sqrt{(108b)^4}\) | Of course, the square root can also be represented as the power to 1/2. |
| \(\left((108b)^4\right)^\frac{1}{2}\) | Using the power rule, we know that \(\left(a^b\right)^c=a^{b*c}\). Let's apply that. |
| \(\left((108b)^4\right)^\frac{1}{2}=(108b)^{4*\frac{1}{2}}=(108b)^2\) | Now, distribute the exponent. |
| \((108b)^2=108^2*b^2\) | Now, let's simplify 108^2 by doing this. |
| \(108^2=(100+8)(100+8)=10000+800+800+64=11664\) | This, to me, is the easiest way to calculate the square of a number without a calculator. What do you think? |
| \(11664b^2\) | This is your final answer. |
