Question 274530
9^(-1) = 1/9


9^(1/2) = sqrt(9)


9^(-1) * 9^(1/2) becomes (1/9) * sqrt(9) becomes (1/9) * 3 becomes 3/9 becomes 1/3.


your answer should be 1/3.


you can use your calculator to confirm from the original equation.


9^(-1) comes out to be .111111111


9^(1/2) comes out to be 3


.11111111 * 3 = .33333333 which is the same as 1/3.


the basic laws of exponents are this:


{{{x^(1/n) = root(n,x)}}} (the numerator in the exponent is 1)


{{{x^(-n) = 1/x^n}}}


{{{x^(k/n) = (root(n,x))^k = root(n,x^k)}}} (the numerator in the exponent is k)