Simplify (x^-4*x)^(5/6)

${(x^{- 4} \cdot x)}^{\frac{5}{6}}$

Multiply $x^{- 4}$ by $x$ by adding the exponents.

Multiply $x^{- 4}$ by $x$ .

Raise $x$ to the power of $1$ .

${(x^{- 4} \cdot x^{1})}^{\frac{5}{6}}$

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

${(x^{- 4 + 1})}^{\frac{5}{6}}$

Add $- 4$ and $1$ .

${(x^{- 3})}^{\frac{5}{6}}$

Multiply the exponents in ${(x^{- 3})}^{\frac{5}{6}}$ .

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

$x^{- 3 (\frac{5}{6})}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$x^{3 (- 1) \frac{5}{6}}$

Factor $3$ out of $6$ .

$x^{3 \cdot - 1 \frac{5}{3 \cdot 2}}$

Cancel the common factor.

$x^{3 \cdot - 1 \frac{5}{3 \cdot 2}}$

Rewrite the expression.

$x^{- \frac{5}{2}}$

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

$\frac{1}{x^{\frac{5}{2}}}$