Simplify the Radical Expression (u^-3*u^-8)^(3/44)

${(u^{- 3} \cdot u^{- 8})}^{\frac{3}{44}}$

Multiply $u^{- 3}$ by $u^{- 8}$ by adding the exponents.

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

${(u^{- 3 - 8})}^{\frac{3}{44}}$

Subtract $8$ from $- 3$ .

${(u^{- 11})}^{\frac{3}{44}}$

Multiply the exponents in ${(u^{- 11})}^{\frac{3}{44}}$ .

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

$u^{- 11 (\frac{3}{44})}$

Cancel the common factor of $11$ .

Factor $11$ out of $- 11$ .

$u^{11 (- 1) \frac{3}{44}}$

Factor $11$ out of $44$ .

$u^{11 \cdot - 1 \frac{3}{11 \cdot 4}}$

Cancel the common factor.

$u^{11 \cdot - 1 \frac{3}{11 \cdot 4}}$

Rewrite the expression.

$u^{- \frac{3}{4}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{u^{\frac{3}{4}}}$