Simplify (9/(144x^4))^(1/2)

${(\frac{9}{144 x^{4}})}^{\frac{1}{2}}$

Step 1

Cancel the common factor of $9$ and $144$ .

Factor $9$ out of $9$ .

${(\frac{9 (1)}{144 x^{4}})}^{\frac{1}{2}}$

Cancel the common factors.

Factor $9$ out of $144 x^{4}$ .

${(\frac{9 (1)}{9 (16 x^{4})})}^{\frac{1}{2}}$

Cancel the common factor.

${(\frac{9 \cdot 1}{9 (16 x^{4})})}^{\frac{1}{2}}$

Rewrite the expression.

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

Step 2

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

Apply the product rule to $\frac{1}{16 x^{4}}$ .

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

Apply the product rule to $16 x^{4}$ .

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

Step 3

One to any power is one.

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

Step 4

Simplify the denominator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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