Simplify (x^8y^-6z^-2)^(1/2)

${(x^{8} y^{- 6} z^{- 2})}^{\frac{1}{2}}$

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

${(x^{8} \frac{1}{y^{6}} z^{- 2})}^{\frac{1}{2}}$

Combine $x^{8}$ and $\frac{1}{y^{6}}$ .

${(\frac{x^{8}}{y^{6}} z^{- 2})}^{\frac{1}{2}}$

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

${(\frac{x^{8}}{y^{6}} \cdot \frac{1}{z^{2}})}^{\frac{1}{2}}$

Combine.

${(\frac{x^{8} \cdot 1}{y^{6} z^{2}})}^{\frac{1}{2}}$

Multiply $x^{8}$ by $1$ .

${(\frac{x^{8}}{y^{6} z^{2}})}^{\frac{1}{2}}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{x^{8}}{y^{6} z^{2}}$ .

$\frac{{(x^{8})}^{\frac{1}{2}}}{{(y^{6} z^{2})}^{\frac{1}{2}}}$

Apply the product rule to $y^{6} z^{2}$ .

$\frac{{(x^{8})}^{\frac{1}{2}}}{{(y^{6})}^{\frac{1}{2}} {(z^{2})}^{\frac{1}{2}}}$

Multiply the exponents in ${(x^{8})}^{\frac{1}{2}}$ .

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

$\frac{x^{8 (\frac{1}{2})}}{{(y^{6})}^{\frac{1}{2}} {(z^{2})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{x^{2 (4) \frac{1}{2}}}{{(y^{6})}^{\frac{1}{2}} {(z^{2})}^{\frac{1}{2}}}$

Cancel the common factor.

$\frac{x^{2 \cdot 4 \frac{1}{2}}}{{(y^{6})}^{\frac{1}{2}} {(z^{2})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{x^{4}}{{(y^{6})}^{\frac{1}{2}} {(z^{2})}^{\frac{1}{2}}}$

Simplify the denominator.

Multiply the exponents in ${(y^{6})}^{\frac{1}{2}}$ .

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

$\frac{x^{4}}{y^{6 (\frac{1}{2})} {(z^{2})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{x^{4}}{y^{2 (3) \frac{1}{2}} {(z^{2})}^{\frac{1}{2}}}$

Cancel the common factor.

$\frac{x^{4}}{y^{2 \cdot 3 \frac{1}{2}} {(z^{2})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{x^{4}}{y^{3} {(z^{2})}^{\frac{1}{2}}}$

Multiply the exponents in ${(z^{2})}^{\frac{1}{2}}$ .

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

$\frac{x^{4}}{y^{3} z^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x^{4}}{y^{3} z^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{x^{4}}{y^{3} z^{1}}$

Simplify.

$\frac{x^{4}}{y^{3} z}$

Simplify (x^8y^-6z^-2)^(1/2)

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