Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the expression.

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Step 3.1

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

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

Step 3.2

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

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

Step 4

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

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

Step 5

Combine fractions.

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Step 5.1

Combine.

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

Step 5.2

Multiply $8$ by $1$ .

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

Step 6

Simplify the denominator.

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Step 6.1

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

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

Step 6.2

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

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

Step 6.3

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

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Step 6.3.1

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

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

Step 6.3.2

Multiply $2$ by $2$ .

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

Step 6.4

Multiply $p^{3}$ by $p^{4}$ by adding the exponents.

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Step 6.4.1

Move $p^{4}$ .

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

Step 6.4.2

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

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

Step 6.4.3

Add $4$ and $3$ .

$\frac{8}{p^{7} \cdot 25}$

Step 7

Move $25$ to the left of $p^{7}$ .

$\frac{8}{25 p^{7}}$