Algebra Examples

$\frac{{(2 (p m^{- 1}) q^{0})}^{- 4} \cdot (2 m^{- 1} p^{3})}{2 p q^{2}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Move ${(2 (p m^{- 1}) q^{0})}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 m^{- 1} p^{3}}{2 p q^{2} {(2 (p m^{- 1}) q^{0})}^{4}}$

Step 1.2

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

$\frac{2 p^{3}}{2 p q^{2} {(2 (p m^{- 1}) q^{0})}^{4} m}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Cancel the common factor.

$\frac{2 p^{3}}{2 p q^{2} {(2 (p m^{- 1}) q^{0})}^{4} m}$

Step 1.3.2

Rewrite the expression.

$\frac{p^{3}}{p q^{2} {(2 (p m^{- 1}) q^{0})}^{4} m}$

Step 1.4

Cancel the common factor of $p^{3}$ and $p$ .

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Step 1.4.1

Factor $p$ out of $p^{3}$ .

$\frac{p \cdot p^{2}}{p q^{2} {(2 (p m^{- 1}) q^{0})}^{4} m}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $p$ out of $p q^{2} {(2 (p m^{- 1}) q^{0})}^{4} m$ .

$\frac{p \cdot p^{2}}{p (q^{2} {(2 (p m^{- 1}) q^{0})}^{4} m)}$

Step 1.4.2.2

Cancel the common factor.

$\frac{p \cdot p^{2}}{p (q^{2} {(2 (p m^{- 1}) q^{0})}^{4} m)}$

Step 1.4.2.3

Rewrite the expression.

$\frac{p^{2}}{q^{2} {(2 (p m^{- 1}) q^{0})}^{4} m}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 p m^{- 1} q^{0}$ .

$\frac{p^{2}}{q^{2} {(2 p m^{- 1})}^{4} {(q^{0})}^{4} m}$

Step 2.2

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

$\frac{p^{2}}{q^{2} {(2 p \frac{1}{m})}^{4} {(q^{0})}^{4} m}$

Step 2.3

Multiply $2 p \frac{1}{m}$ .

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Step 2.3.1

Combine $2$ and $\frac{1}{m}$ .

$\frac{p^{2}}{q^{2} {(p \frac{2}{m})}^{4} {(q^{0})}^{4} m}$

Step 2.3.2

Combine $p$ and $\frac{2}{m}$ .

$\frac{p^{2}}{q^{2} {(\frac{p \cdot 2}{m})}^{4} {(q^{0})}^{4} m}$

Step 2.4

Move $2$ to the left of $p$ .

$\frac{p^{2}}{q^{2} {(\frac{2 \cdot p}{m})}^{4} {(q^{0})}^{4} m}$

Step 2.5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.5.1

Apply the product rule to $\frac{2 p}{m}$ .

$\frac{p^{2}}{q^{2} \frac{{(2 p)}^{4}}{m^{4}} {(q^{0})}^{4} m}$

Step 2.5.2

Apply the product rule to $2 p$ .

$\frac{p^{2}}{q^{2} \frac{2^{4} p^{4}}{m^{4}} {(q^{0})}^{4} m}$

Step 2.6

Raise $2$ to the power of $4$ .

$\frac{p^{2}}{q^{2} \frac{16 p^{4}}{m^{4}} {(q^{0})}^{4} m}$

Step 2.7

Multiply the exponents in ${(q^{0})}^{4}$ .

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Step 2.7.1

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

$\frac{p^{2}}{q^{2} \frac{16 p^{4}}{m^{4}} q^{0 \cdot 4} m}$

Step 2.7.2

Multiply $0$ by $4$ .

$\frac{p^{2}}{q^{2} \frac{16 p^{4}}{m^{4}} q^{0} m}$

Step 2.8

Anything raised to $0$ is $1$ .

$\frac{p^{2}}{q^{2} \frac{16 p^{4}}{m^{4}} \cdot 1 m}$

Step 2.9

Combine exponents.

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Step 2.9.1

Combine $q^{2}$ and $\frac{16 p^{4}}{m^{4}}$ .

$\frac{p^{2}}{\frac{q^{2} (16 p^{4})}{m^{4}} \cdot 1 m}$

Step 2.9.2

Multiply $\frac{q^{2} (16 p^{4})}{m^{4}}$ by $1$ .

$\frac{p^{2}}{\frac{q^{2} (16 p^{4})}{m^{4}} m}$

Step 2.9.3

Combine $\frac{q^{2} (16 p^{4})}{m^{4}}$ and $m$ .

$\frac{p^{2}}{\frac{q^{2} (16 p^{4}) m}{m^{4}}}$

Step 2.10

Remove unnecessary parentheses.

$\frac{p^{2}}{\frac{q^{2} \cdot 16 p^{4} m}{m^{4}}}$

Step 2.11

Reduce the expression $\frac{q^{2} \cdot 16 p^{4} m}{m^{4}}$ by cancelling the common factors.

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Step 2.11.1

Factor $m$ out of $q^{2} \cdot 16 p^{4} m$ .

$\frac{p^{2}}{\frac{m (q^{2} \cdot 16 p^{4})}{m^{4}}}$

Step 2.11.2

Factor $m$ out of $m^{4}$ .

$\frac{p^{2}}{\frac{m (q^{2} \cdot 16 p^{4})}{m \cdot m^{3}}}$

Step 2.11.3

Cancel the common factor.

$\frac{p^{2}}{\frac{m (q^{2} \cdot 16 p^{4})}{m \cdot m^{3}}}$

Step 2.11.4

Rewrite the expression.

$\frac{p^{2}}{\frac{q^{2} \cdot 16 p^{4}}{m^{3}}}$

Step 2.12

Move $16$ to the left of $q^{2}$ .

$\frac{p^{2}}{\frac{16 q^{2} p^{4}}{m^{3}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$p^{2} \frac{m^{3}}{16 q^{2} p^{4}}$

Step 4

Cancel the common factor of $p^{2}$ .

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Step 4.1

Factor $p^{2}$ out of $16 q^{2} p^{4}$ .

$p^{2} \frac{m^{3}}{p^{2} (16 q^{2} p^{2})}$

Step 4.2

Cancel the common factor.

$p^{2} \frac{m^{3}}{p^{2} (16 q^{2} p^{2})}$

Step 4.3

Rewrite the expression.

$\frac{m^{3}}{16 q^{2} p^{2}}$