Algebra Examples

${(\frac{a^{2} b^{- 3}}{c^{4}})}^{- \frac{1}{2}}$

Step 1

Move $b^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{a^{2}}{c^{4} b^{3}})}^{- \frac{1}{2}}$

Step 2

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

${(\frac{c^{4} b^{3}}{a^{2}})}^{\frac{1}{2}}$

Step 3

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

Tap for more steps...

Step 3.1

Apply the product rule to $\frac{c^{4} b^{3}}{a^{2}}$ .

$\frac{{(c^{4} b^{3})}^{\frac{1}{2}}}{{(a^{2})}^{\frac{1}{2}}}$

Step 3.2

Apply the product rule to $c^{4} b^{3}$ .

$\frac{{(c^{4})}^{\frac{1}{2}} {(b^{3})}^{\frac{1}{2}}}{{(a^{2})}^{\frac{1}{2}}}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

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

$\frac{c^{4 (\frac{1}{2})} {(b^{3})}^{\frac{1}{2}}}{{(a^{2})}^{\frac{1}{2}}}$

Step 4.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.2.1

Factor $2$ out of $4$ .

$\frac{c^{2 (2) \frac{1}{2}} {(b^{3})}^{\frac{1}{2}}}{{(a^{2})}^{\frac{1}{2}}}$

Step 4.1.2.2

Cancel the common factor.

$\frac{c^{2 \cdot 2 \frac{1}{2}} {(b^{3})}^{\frac{1}{2}}}{{(a^{2})}^{\frac{1}{2}}}$

Step 4.1.2.3

Rewrite the expression.

$\frac{c^{2} {(b^{3})}^{\frac{1}{2}}}{{(a^{2})}^{\frac{1}{2}}}$

Step 4.2

Multiply the exponents in ${(b^{3})}^{\frac{1}{2}}$ .

Tap for more steps...

Step 4.2.1

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

$\frac{c^{2} b^{3 (\frac{1}{2})}}{{(a^{2})}^{\frac{1}{2}}}$

Step 4.2.2

Combine $3$ and $\frac{1}{2}$ .

$\frac{c^{2} b^{\frac{3}{2}}}{{(a^{2})}^{\frac{1}{2}}}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

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

$\frac{c^{2} b^{\frac{3}{2}}}{a^{2 (\frac{1}{2})}}$

Step 5.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.1.2.1

Cancel the common factor.

$\frac{c^{2} b^{\frac{3}{2}}}{a^{2 (\frac{1}{2})}}$

Step 5.1.2.2

Rewrite the expression.

$\frac{c^{2} b^{\frac{3}{2}}}{a^{1}}$

Step 5.2

Simplify.

$\frac{c^{2} b^{\frac{3}{2}}}{a}$