Simplify ((25x^4)/(16y^6))^(-1/2)

${(\frac{25 x^{4}}{16 y^{6}})}^{- \frac{1}{2}}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{16 y^{6}}{25 x^{4}})}^{\frac{1}{2}}$

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

Apply the product rule to $\frac{16 y^{6}}{25 x^{4}}$ .

$\frac{{(16 y^{6})}^{\frac{1}{2}}}{{(25 x^{4})}^{\frac{1}{2}}}$

Apply the product rule to $16 y^{6}$ .

$\frac{16^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}}{{(25 x^{4})}^{\frac{1}{2}}}$

Apply the product rule to $25 x^{4}$ .

$\frac{16^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

$\frac{{(4^{2})}^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

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

$\frac{4^{2 (\frac{1}{2})} {(y^{6})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4^{2 (\frac{1}{2})} {(y^{6})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{4^{1} {(y^{6})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{4 {(y^{6})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

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

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

$\frac{4 y^{6 (\frac{1}{2})}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{4 y^{2 (3) \frac{1}{2}}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

Cancel the common factor.

$\frac{4 y^{2 \cdot 3 \frac{1}{2}}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{4 y^{3}}{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$\frac{4 y^{3}}{{(5^{2})}^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}$

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

$\frac{4 y^{3}}{5^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 y^{3}}{5^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{4 y^{3}}{5^{1} {(x^{4})}^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{4 y^{3}}{5 {(x^{4})}^{\frac{1}{2}}}$

Multiply the exponents in ${(x^{4})}^{\frac{1}{2}}$ .

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

$\frac{4 y^{3}}{5 x^{4 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{4 y^{3}}{5 x^{2 (2) \frac{1}{2}}}$

Cancel the common factor.

$\frac{4 y^{3}}{5 x^{2 \cdot 2 \frac{1}{2}}}$

Rewrite the expression.

$\frac{4 y^{3}}{5 x^{2}}$

Simplify ((25x^4)/(16y^6))^(-1/2)

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