Precalculus Examples

$\frac{24 a^{2} b^{3} c}{16 a b^{- 1} c^{2}}$

Step 1

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

$\frac{24 a^{2} b^{3} c b}{16 a c^{2}}$

Step 2

Multiply $b^{3}$ by $b$ by adding the exponents.

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Step 2.1

Move $b$ .

$\frac{24 a^{2} (b \cdot b^{3}) c}{16 a c^{2}}$

Step 2.2

Multiply $b$ by $b^{3}$ .

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Step 2.2.1

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

$\frac{24 a^{2} (b^{1} b^{3}) c}{16 a c^{2}}$

Step 2.2.2

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

$\frac{24 a^{2} b^{1 + 3} c}{16 a c^{2}}$

$\frac{24 a^{2} b^{1 + 3} c}{16 a c^{2}}$

Step 2.3

Add $1$ and $3$ .

$\frac{24 a^{2} b^{4} c}{16 a c^{2}}$

$\frac{24 a^{2} b^{4} c}{16 a c^{2}}$

Step 3

Cancel the common factor of $24$ and $16$ .

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Step 3.1

Factor $8$ out of $24 a^{2} b^{4} c$ .

$\frac{8 (3 a^{2} b^{4} c)}{16 a c^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $8$ out of $16 a c^{2}$ .

$\frac{8 (3 a^{2} b^{4} c)}{8 (2 a c^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{8 (3 a^{2} b^{4} c)}{8 (2 a c^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{3 a^{2} b^{4} c}{2 a c^{2}}$

$\frac{3 a^{2} b^{4} c}{2 a c^{2}}$

$\frac{3 a^{2} b^{4} c}{2 a c^{2}}$

Step 4

Cancel the common factor of $a^{2}$ and $a$ .

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Step 4.1

Factor $a$ out of $3 a^{2} b^{4} c$ .

$\frac{a (3 a b^{4} c)}{2 a c^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a$ out of $2 a c^{2}$ .

$\frac{a (3 a b^{4} c)}{a (2 c^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{a (3 a b^{4} c)}{a (2 c^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{3 a b^{4} c}{2 c^{2}}$

$\frac{3 a b^{4} c}{2 c^{2}}$

$\frac{3 a b^{4} c}{2 c^{2}}$

Step 5

Cancel the common factor of $c$ and $c^{2}$ .

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Step 5.1

Factor $c$ out of $3 a b^{4} c$ .

$\frac{c (3 a b^{4})}{2 c^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $c$ out of $2 c^{2}$ .

$\frac{c (3 a b^{4})}{c (2 c)}$

Step 5.2.2

Cancel the common factor.

$\frac{c (3 a b^{4})}{c (2 c)}$

Step 5.2.3

Rewrite the expression.

$\frac{3 a b^{4}}{2 c}$

$\frac{3 a b^{4}}{2 c}$

$\frac{3 a b^{4}}{2 c}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$