Simplify (x^12y^10)^(-1/2)

${(x^{12} y^{10})}^{- \frac{1}{2}}$

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

$\frac{1}{{(x^{12} y^{10})}^{\frac{1}{2}}}$

Simplify the denominator.

Apply the product rule to $x^{12} y^{10}$ .

$\frac{1}{{(x^{12})}^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Multiply the exponents in ${(x^{12})}^{\frac{1}{2}}$ .

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

$\frac{1}{x^{12 (\frac{1}{2})} {(y^{10})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

$\frac{1}{x^{2 (6) \frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Cancel the common factor.

$\frac{1}{x^{2 \cdot 6 \frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{1}{x^{6} {(y^{10})}^{\frac{1}{2}}}$

Multiply the exponents in ${(y^{10})}^{\frac{1}{2}}$ .

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

$\frac{1}{x^{6} y^{10 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$\frac{1}{x^{6} y^{2 (5) \frac{1}{2}}}$

Cancel the common factor.

$\frac{1}{x^{6} y^{2 \cdot 5 \frac{1}{2}}}$

Rewrite the expression.

$\frac{1}{x^{6} y^{5}}$