Basic Math Examples

$\frac{v - 1}{v^{4} \cdot {(v^{- \frac{1}{4}})}^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

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

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Step 1.1.1

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

$\frac{v - 1}{v^{4} v^{- \frac{1}{4} \cdot 2}}$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{v - 1}{v^{4} v^{\frac{- 1}{4} \cdot 2}}$

Step 1.1.2.2

Factor $2$ out of $4$ .

$\frac{v - 1}{v^{4} v^{\frac{- 1}{2 (2)} \cdot 2}}$

Step 1.1.2.3

Cancel the common factor.

$\frac{v - 1}{v^{4} v^{\frac{- 1}{2 \cdot 2} \cdot 2}}$

Step 1.1.2.4

Rewrite the expression.

$\frac{v - 1}{v^{4} v^{\frac{- 1}{2}}}$

Step 1.1.3

Move the negative in front of the fraction.

$\frac{v - 1}{v^{4} v^{- \frac{1}{2}}}$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{v - 1}{v^{4} \frac{1}{v^{\frac{1}{2}}}}$

Step 2

Combine $v^{4}$ and $\frac{1}{v^{\frac{1}{2}}}$ .

$\frac{v - 1}{\frac{v^{4}}{v^{\frac{1}{2}}}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Move $v^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{v - 1}{v^{4} v^{- \frac{1}{2}}}$

Step 3.2

Multiply $v^{4}$ by $v^{- \frac{1}{2}}$ by adding the exponents.

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Step 3.2.1

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

$\frac{v - 1}{v^{4 - \frac{1}{2}}}$

Step 3.2.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{v - 1}{v^{4 \cdot \frac{2}{2} - \frac{1}{2}}}$

Step 3.2.3

Combine $4$ and $\frac{2}{2}$ .

$\frac{v - 1}{v^{\frac{4 \cdot 2}{2} - \frac{1}{2}}}$

Step 3.2.4

Combine the numerators over the common denominator.

$\frac{v - 1}{v^{\frac{4 \cdot 2 - 1}{2}}}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $4$ by $2$ .

$\frac{v - 1}{v^{\frac{8 - 1}{2}}}$

Step 3.2.5.2

Subtract $1$ from $8$ .

$\frac{v - 1}{v^{\frac{7}{2}}}$