Basic Math Examples

${(\frac{r^{\frac{1}{4}} y^{- 5}}{r^{- 1}})}^{- 4}$

Step 1

Move $y^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{r^{\frac{1}{4}}}{r^{- 1} y^{5}})}^{- 4}$

Step 2

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

${(\frac{r^{\frac{1}{4}} r}{y^{5}})}^{- 4}$

Step 3

Multiply $r^{\frac{1}{4}}$ by $r$ by adding the exponents.

Tap for more steps...

Step 3.1

Multiply $r^{\frac{1}{4}}$ by $r$ .

Tap for more steps...

Step 3.1.1

Raise $r$ to the power of $1$ .

${(\frac{r^{\frac{1}{4}} r^{1}}{y^{5}})}^{- 4}$

Step 3.1.2

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

${(\frac{r^{\frac{1}{4} + 1}}{y^{5}})}^{- 4}$

Step 3.2

Write $1$ as a fraction with a common denominator.

${(\frac{r^{\frac{1}{4} + \frac{4}{4}}}{y^{5}})}^{- 4}$

Step 3.3

Combine the numerators over the common denominator.

${(\frac{r^{\frac{1 + 4}{4}}}{y^{5}})}^{- 4}$

Step 3.4

Add $1$ and $4$ .

${(\frac{r^{\frac{5}{4}}}{y^{5}})}^{- 4}$

Step 4

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

${(\frac{y^{5}}{r^{\frac{5}{4}}})}^{4}$

Step 5

Apply the product rule to $\frac{y^{5}}{r^{\frac{5}{4}}}$ .

$\frac{{(y^{5})}^{4}}{{(r^{\frac{5}{4}})}^{4}}$

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

Multiply $5$ by $4$ .

$\frac{y^{20}}{{(r^{\frac{5}{4}})}^{4}}$

Step 7

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

Tap for more steps...

Step 7.1

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

$\frac{y^{20}}{r^{\frac{5}{4} \cdot 4}}$

Step 7.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 7.2.1

Cancel the common factor.

$\frac{y^{20}}{r^{\frac{5}{4} \cdot 4}}$

Step 7.2.2

Rewrite the expression.

$\frac{y^{20}}{r^{5}}$