# Which expression is equivalent to the given expression?

## Answers

Choice C. is equivalent.Let's first simplify, starting with the denominator. a to the power of 0 is 1. —> any value to the power of 0 is 1.That leaves us with (1b^2)^4. Now we can distribute the exponent. But before that, let's get rid of the coefficient 1, which isn't necessary.Now we are left with (b^2)^4.Let's use the power of the power rule, which means that we multiply the exponent by the exponent. The denominator is now b^8.Looking at the numerator, there is a b, which has a hidden exponent of one. —> We can get rid of it by taking away its exponent of 1 with the b^8 from the denomiator. . . . b^1 goes away, and b^8 becomes b^7.We cannot simplify any further, therefore the final expression is. . .6a/b^7.

Step-by-step explanation:[tex]( \frac{6ab}{(a {}^{0} {b}^{2} ) {}^{4} } ) \\ \\ =( \frac{6ab}{1 \times {b}^{8} } ) \\ \\ = \frac{6a}{ {b}^{7} } [/tex]