Basic Math Examples

${(v^{\frac{1}{2}} \cdot y^{- 2})}^{\frac{5}{4}}$

Step 1

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

${(v^{\frac{1}{2}} \cdot \frac{1}{y^{2}})}^{\frac{5}{4}}$

Step 2

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

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

Step 3

Apply basic rules of exponents.

Tap for more steps...

Step 3.1

Apply the product rule to $\frac{v^{\frac{1}{2}}}{y^{2}}$ .

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

Step 3.2

Multiply the exponents in ${(v^{\frac{1}{2}})}^{\frac{5}{4}}$ .

Tap for more steps...

Step 3.2.1

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

$\frac{v^{\frac{1}{2} \cdot \frac{5}{4}}}{{(y^{2})}^{\frac{5}{4}}}$

Step 3.2.2

Multiply $\frac{1}{2} \cdot \frac{5}{4}$ .

Tap for more steps...

Step 3.2.2.1

Multiply $\frac{1}{2}$ by $\frac{5}{4}$ .

$\frac{v^{\frac{5}{2 \cdot 4}}}{{(y^{2})}^{\frac{5}{4}}}$

Step 3.2.2.2

Multiply $2$ by $4$ .

$\frac{v^{\frac{5}{8}}}{{(y^{2})}^{\frac{5}{4}}}$

Step 3.3

Multiply the exponents in ${(y^{2})}^{\frac{5}{4}}$ .

Tap for more steps...

Step 3.3.1

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

$\frac{v^{\frac{5}{8}}}{y^{2 (\frac{5}{4})}}$

Step 3.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.2.1

Factor $2$ out of $4$ .

$\frac{v^{\frac{5}{8}}}{y^{2 \frac{5}{2 (2)}}}$

Step 3.3.2.2

Cancel the common factor.

$\frac{v^{\frac{5}{8}}}{y^{2 \frac{5}{2 \cdot 2}}}$

Step 3.3.2.3

Rewrite the expression.

$\frac{v^{\frac{5}{8}}}{y^{\frac{5}{2}}}$