Basic Math Examples

${(2 p^{- 1})}^{- 3} {(5 p^{2})}^{- 2}$

Step 1

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

${(2 \frac{1}{p})}^{- 3} {(5 p^{2})}^{- 2}$

Step 2

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

${(\frac{2}{p})}^{- 3} {(5 p^{2})}^{- 2}$

Step 3

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

${(\frac{p}{2})}^{3} {(5 p^{2})}^{- 2}$

Step 4

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

$\frac{p^{3}}{2^{3}} {(5 p^{2})}^{- 2}$

Step 5

Raise $2$ to the power of $3$ .

$\frac{p^{3}}{8} {(5 p^{2})}^{- 2}$

Step 6

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

$\frac{p^{3}}{8} \cdot \frac{1}{{(5 p^{2})}^{2}}$

Step 7

Combine fractions.

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Step 7.1

Combine.

$\frac{p^{3} \cdot 1}{8 {(5 p^{2})}^{2}}$

Step 7.2

Multiply $p^{3}$ by $1$ .

$\frac{p^{3}}{8 {(5 p^{2})}^{2}}$

Step 8

Simplify the denominator.

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Step 8.1

Apply the product rule to $5 p^{2}$ .

$\frac{p^{3}}{8 \cdot 5^{2} {(p^{2})}^{2}}$

Step 8.2

Raise $5$ to the power of $2$ .

$\frac{p^{3}}{8 \cdot 25 {(p^{2})}^{2}}$

Step 8.3

Multiply the exponents in ${(p^{2})}^{2}$ .

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Step 8.3.1

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

$\frac{p^{3}}{8 \cdot 25 p^{2 \cdot 2}}$

Step 8.3.2

Multiply $2$ by $2$ .

$\frac{p^{3}}{8 \cdot 25 p^{4}}$

Step 8.4

Multiply $8$ by $25$ .

$\frac{p^{3}}{200 p^{4}}$

Step 9

Cancel the common factor of $p^{3}$ and $p^{4}$ .

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Step 9.1

Multiply by $1$ .

$\frac{p^{3} \cdot 1}{200 p^{4}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $p^{3}$ out of $200 p^{4}$ .

$\frac{p^{3} \cdot 1}{p^{3} (200 p)}$

Step 9.2.2

Cancel the common factor.

$\frac{p^{3} \cdot 1}{p^{3} (200 p)}$

Step 9.2.3

Rewrite the expression.

$\frac{1}{200 p}$