Simplify ((36c^6)/(25y^8))^(-1/2)

${(\frac{36 c^{6}}{25 y^{8}})}^{\frac{- 1}{2}}$

Step 1

Move the negative in front of the fraction.

${(\frac{36 c^{6}}{25 y^{8}})}^{- \frac{1}{2}}$

Step 2

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

${(\frac{25 y^{8}}{36 c^{6}})}^{\frac{1}{2}}$

Step 3

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

Apply the product rule to $\frac{25 y^{8}}{36 c^{6}}$ .

$\frac{{(25 y^{8})}^{\frac{1}{2}}}{{(36 c^{6})}^{\frac{1}{2}}}$

Apply the product rule to $25 y^{8}$ .

$\frac{25^{\frac{1}{2}} {(y^{8})}^{\frac{1}{2}}}{{(36 c^{6})}^{\frac{1}{2}}}$

Apply the product rule to $36 c^{6}$ .

$\frac{25^{\frac{1}{2}} {(y^{8})}^{\frac{1}{2}}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

Step 4

Simplify the numerator.

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

$\frac{{(5^{2})}^{\frac{1}{2}} {(y^{8})}^{\frac{1}{2}}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

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

$\frac{5^{2 (\frac{1}{2})} {(y^{8})}^{\frac{1}{2}}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{1}{2})} {(y^{8})}^{\frac{1}{2}}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{5^{1} {(y^{8})}^{\frac{1}{2}}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{5 {(y^{8})}^{\frac{1}{2}}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

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

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

$\frac{5 y^{8 (\frac{1}{2})}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{5 y^{2 (4) \frac{1}{2}}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

Cancel the common factor.

$\frac{5 y^{2 \cdot 4 \frac{1}{2}}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{5 y^{4}}{36^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

Step 5

Simplify the denominator.

Rewrite $36$ as $6^{2}$ .

$\frac{5 y^{4}}{{(6^{2})}^{\frac{1}{2}} {(c^{6})}^{\frac{1}{2}}}$

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

$\frac{5 y^{4}}{6^{2 (\frac{1}{2})} {(c^{6})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 y^{4}}{6^{2 (\frac{1}{2})} {(c^{6})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{5 y^{4}}{6^{1} {(c^{6})}^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{5 y^{4}}{6 {(c^{6})}^{\frac{1}{2}}}$

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

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

$\frac{5 y^{4}}{6 c^{6 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{5 y^{4}}{6 c^{2 (3) \frac{1}{2}}}$

Cancel the common factor.

$\frac{5 y^{4}}{6 c^{2 \cdot 3 \frac{1}{2}}}$

Rewrite the expression.

$\frac{5 y^{4}}{6 c^{3}}$

Simplify ((36c^6)/(25y^8))^(-1/2)

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