Question

Simplify the following expression to simplest form using only positive exponents. 5

Answer 1

`(16y^(28))/(x^(16))`

Step-by-step explanation:

Exponent rule :

`(a*b)^n\text{ = a}^2b^n`

`(32x^(-20)y^(35))^{-(4)/(5)}=\text{ 32}^{(4)/(5)}(x^(-20))^{(4)/(5)}(y^(35))^{(4)/(5)}`

Since

`32^{(4)/(5)}\text{ = 16}`

You can replace it in the equation

`16(x^(-20))^{(4)/(5)}(y^(35))^{(4)/(5)}`

Since

`Simplified\text{ : }(x^(-20))^{(4)/(5)}\text{ = }(1)/(x^(16))`
`Simplified\text{ : \lparen}y^(35))^{(4)/(5)}\text{ = }y^(28)`

You can replace them in the equation

`16*(1)/(x^(16))*y^(28)\text{ = }(16y^(28))/(x^(16))`