Question

Take the answer: 8^2/9 . Create an expression using each of the specified properties below that will result in this answer once it is simplifieda. Product of Powersb. Power of a Powerc. Quotient of Powers

Answer 1

For the value given

`8^{(2)/(9)}`

To create the expressions required in the question, we will follow the steps below

Part A: Product of powers

`a^m* a^n=a^(m+n)`

hence

`8^{(2)/(9)}=8^{(1)/(9)}*8^{(1)/(9)}`

Part B: Power of power

`(a^m)^n=a^(m* n)`

Thus

`8^{(2)/(9)}=(8^{(1)/(9)})^2`

Part C: Quotient of powers

`8^{(2)/(9)}=\frac{8^1}{8^{(7)/(9)}}`