Question

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

Answer 1

$(\frac{2p}{q^{2}}) ^{3} (\frac{3p^{4}}{q^{-4}})^{-1}$  Multiply the outside exponent into each

$(\frac{2p^{3}}{q^{6}} )(\frac{3p^{-4}}{q^{4}} )$  Multiply together

$\frac{6p^{-1}}{q^{10}} = \frac{1}{q^{10}6p^{1}}$

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:

$x^{-2} = \frac{1}{x^{2}}$

$\frac{x}{y^{-1}} = x(y^1)$

$\frac{1}{y^{-2}} = y^2$

Sorry if this is confusing