Algebra Examples

$\frac{b^{3}}{c^{\frac{1}{2}}} \cdot \frac{c}{b^{\frac{1}{3}}}$

Step 1

Combine.

$\frac{b^{3} c}{c^{\frac{1}{2}} b^{\frac{1}{3}}}$

Step 2

Move $b^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{b^{3} c b^{- \frac{1}{3}}}{c^{\frac{1}{2}}}$

Step 3

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

$b^{3} c b^{- \frac{1}{3}} c^{- \frac{1}{2}}$

Step 4

Multiply $b^{3}$ by $b^{- \frac{1}{3}}$ by adding the exponents.

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Step 4.1

Move $b^{- \frac{1}{3}}$ .

$b^{- \frac{1}{3}} b^{3} c \cdot c^{- \frac{1}{2}}$

Step 4.2

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

$b^{- \frac{1}{3} + 3} c \cdot c^{- \frac{1}{2}}$

Step 4.3

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b^{- \frac{1}{3} + 3 \cdot \frac{3}{3}} c \cdot c^{- \frac{1}{2}}$

Step 4.4

Combine $3$ and $\frac{3}{3}$ .

$b^{- \frac{1}{3} + \frac{3 \cdot 3}{3}} c \cdot c^{- \frac{1}{2}}$

Step 4.5

Combine the numerators over the common denominator.

$b^{\frac{- 1 + 3 \cdot 3}{3}} c \cdot c^{- \frac{1}{2}}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $3$ by $3$ .

$b^{\frac{- 1 + 9}{3}} c \cdot c^{- \frac{1}{2}}$

Step 4.6.2

Add $- 1$ and $9$ .

$b^{\frac{8}{3}} c \cdot c^{- \frac{1}{2}}$

Step 5

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

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Step 5.1

Move $c^{- \frac{1}{2}}$ .

$b^{\frac{8}{3}} (c^{- \frac{1}{2}} c)$

Step 5.2

Multiply $c^{- \frac{1}{2}}$ by $c$ .

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Step 5.2.1

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

$b^{\frac{8}{3}} (c^{- \frac{1}{2}} c^{1})$

Step 5.2.2

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

$b^{\frac{8}{3}} c^{- \frac{1}{2} + 1}$

Step 5.3

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

$b^{\frac{8}{3}} c^{- \frac{1}{2} + \frac{2}{2}}$

Step 5.4

Combine the numerators over the common denominator.

$b^{\frac{8}{3}} c^{\frac{- 1 + 2}{2}}$

Step 5.5

Add $- 1$ and $2$ .

$b^{\frac{8}{3}} c^{\frac{1}{2}}$