Basic Math Examples

$\frac{99 r^{\frac{7}{8}}}{11 r^{\frac{6}{5}}}$

Step 1

Move $r^{\frac{7}{8}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{99}{11 r^{\frac{6}{5}} r^{- \frac{7}{8}}}$

Step 2

Multiply $r^{\frac{6}{5}}$ by $r^{- \frac{7}{8}}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $r^{- \frac{7}{8}}$ .

$\frac{99}{11 (r^{- \frac{7}{8}} r^{\frac{6}{5}})}$

Step 2.2

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

$\frac{99}{11 r^{- \frac{7}{8} + \frac{6}{5}}}$

Step 2.3

To write $- \frac{7}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{99}{11 r^{- \frac{7}{8} \cdot \frac{5}{5} + \frac{6}{5}}}$

Step 2.4

To write $\frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{99}{11 r^{- \frac{7}{8} \cdot \frac{5}{5} + \frac{6}{5} \cdot \frac{8}{8}}}$

Step 2.5

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.5.1

Multiply $\frac{7}{8}$ by $\frac{5}{5}$ .

$\frac{99}{11 r^{- \frac{7 \cdot 5}{8 \cdot 5} + \frac{6}{5} \cdot \frac{8}{8}}}$

Step 2.5.2

Multiply $8$ by $5$ .

$\frac{99}{11 r^{- \frac{7 \cdot 5}{40} + \frac{6}{5} \cdot \frac{8}{8}}}$

Step 2.5.3

Multiply $\frac{6}{5}$ by $\frac{8}{8}$ .

$\frac{99}{11 r^{- \frac{7 \cdot 5}{40} + \frac{6 \cdot 8}{5 \cdot 8}}}$

Step 2.5.4

Multiply $5$ by $8$ .

$\frac{99}{11 r^{- \frac{7 \cdot 5}{40} + \frac{6 \cdot 8}{40}}}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{99}{11 r^{\frac{- 7 \cdot 5 + 6 \cdot 8}{40}}}$

Step 2.7

Simplify the numerator.

Tap for more steps...

Step 2.7.1

Multiply $- 7$ by $5$ .

$\frac{99}{11 r^{\frac{- 35 + 6 \cdot 8}{40}}}$

Step 2.7.2

Multiply $6$ by $8$ .

$\frac{99}{11 r^{\frac{- 35 + 48}{40}}}$

Step 2.7.3

Add $- 35$ and $48$ .

$\frac{99}{11 r^{\frac{13}{40}}}$

Step 3

Factor $11$ out of $99$ .

$\frac{11 \cdot 9}{11 r^{\frac{13}{40}}}$

Step 4

Cancel the common factors.

Tap for more steps...

Step 4.1

Factor $11$ out of $11 r^{\frac{13}{40}}$ .

$\frac{11 \cdot 9}{11 (r^{\frac{13}{40}})}$

Step 4.2

Cancel the common factor.

$\frac{11 \cdot 9}{11 r^{\frac{13}{40}}}$

Step 4.3

Rewrite the expression.

$\frac{9}{r^{\frac{13}{40}}}$