Algebra Examples

${(\frac{v^{- 1}}{v^{- 4}})}^{\frac{5}{12}}$

Step 1

Move $v^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(v^{- 1} v^{4})}^{\frac{5}{12}}$

Step 2

Multiply $v^{- 1}$ by $v^{4}$ by adding the exponents.

Tap for more steps...

Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(v^{- 1 + 4})}^{\frac{5}{12}}$

Step 2.2

Add $- 1$ and $4$ .

${(v^{3})}^{\frac{5}{12}}$

Step 3

Multiply the exponents in ${(v^{3})}^{\frac{5}{12}}$ .

Tap for more steps...

Step 3.1

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

$v^{3 (\frac{5}{12})}$

Step 3.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1

Factor $3$ out of $12$ .

$v^{3 \frac{5}{3 (4)}}$

Step 3.2.2

Cancel the common factor.

$v^{3 \frac{5}{3 \cdot 4}}$

Step 3.2.3

Rewrite the expression.

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