Simplify (1/(25x)*x^9)^(-1/2)

${(\frac{1}{25 x} \cdot x^{9})}^{- \frac{1}{2}}$

Step 1

Cancel the common factor of $x$ .

Factor $x$ out of $25 x$ .

${(\frac{1}{x \cdot 25} \cdot x^{9})}^{- \frac{1}{2}}$

Factor $x$ out of $x^{9}$ .

${(\frac{1}{x \cdot 25} \cdot (x \cdot x^{8}))}^{- \frac{1}{2}}$

Cancel the common factor.

${(\frac{1}{x \cdot 25} \cdot (x \cdot x^{8}))}^{- \frac{1}{2}}$

Rewrite the expression.

${(\frac{1}{25} \cdot x^{8})}^{- \frac{1}{2}}$

Step 2

Combine $\frac{1}{25}$ and $x^{8}$ .

${(\frac{x^{8}}{25})}^{- \frac{1}{2}}$

Step 3

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

${(\frac{25}{x^{8}})}^{\frac{1}{2}}$

Step 4

Apply the product rule to $\frac{25}{x^{8}}$ .

$\frac{25^{\frac{1}{2}}}{{(x^{8})}^{\frac{1}{2}}}$

Step 5

Simplify the numerator.

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

$\frac{{(5^{2})}^{\frac{1}{2}}}{{(x^{8})}^{\frac{1}{2}}}$

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

$\frac{5^{2 (\frac{1}{2})}}{{(x^{8})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{1}{2})}}{{(x^{8})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{5^{1}}{{(x^{8})}^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{5}{{(x^{8})}^{\frac{1}{2}}}$

Step 6

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

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

$\frac{5}{x^{8 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5}{x^{4}}$