Question

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero numbers.

Answer 1

`((2p)/(q^(2))) ^(3) ((3p^(4))/(q^(-4)))^(-1)` Multiply the outside exponent into each

`((2p^(3))/(q^(6)) )((3p^(-4))/(q^(4)) )` Multiply together

`(6p^(-1))/(q^(10)) = (1)/(q^(10)6p^(1))`

When you multiply an exponent DIRECTLY into another variable(with an exponent), you multiply the exponents.

For example:

(x²)³ =
`x^(6)`

`(x^(4))^(5) = x^(20)`

When you multiply a variable with an exponent into another variable with an exponent, you add the exponents.

For example:

`(x^(2) )(x^(3) )=x^(5)`

`(x^(1) )(x^(3)) = x^(4)`

First I multiplied the outside exponents into the numerator and the denominator.

When you have a negative exponent, you move it onto the other side of the fraction to make it positive.

For example:

`x^(-2) = (1)/(x^(2))`

`(x)/(y^(-1)) = x(y^1)`

`(1)/(y^(-2)) = y^2`

Sorry if this is confusing