Simplify (q^7*q^-3)^(5/4)

${(q^{7} \cdot q^{- 3})}^{\frac{5}{4}}$

Multiply $q^{7}$ by $q^{- 3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(q^{7 - 3})}^{\frac{5}{4}}$

Subtract $3$ from $7$ .

${(q^{4})}^{\frac{5}{4}}$

Multiply the exponents in ${(q^{4})}^{\frac{5}{4}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$q^{4 (\frac{5}{4})}$

Cancel the common factor of $4$ .

Cancel the common factor.

$q^{4 (\frac{5}{4})}$

Rewrite the expression.

$q^{5}$