Basic Math Examples

${(a^{- 5} b^{7} c^{- 2})}^{3}$

Step 1

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

${(\frac{1}{a^{5}} b^{7} c^{- 2})}^{3}$

Step 2

Combine $\frac{1}{a^{5}}$ and $b^{7}$ .

${(\frac{b^{7}}{a^{5}} c^{- 2})}^{3}$

Step 3

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

${(\frac{b^{7}}{a^{5}} \cdot \frac{1}{c^{2}})}^{3}$

Step 4

Combine.

${(\frac{b^{7} \cdot 1}{a^{5} c^{2}})}^{3}$

Step 5

Multiply $b^{7}$ by $1$ .

${(\frac{b^{7}}{a^{5} c^{2}})}^{3}$

Step 6

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

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Step 6.1

Apply the product rule to $\frac{b^{7}}{a^{5} c^{2}}$ .

$\frac{{(b^{7})}^{3}}{{(a^{5} c^{2})}^{3}}$

Step 6.2

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

$\frac{{(b^{7})}^{3}}{{(a^{5})}^{3} {(c^{2})}^{3}}$

Step 7

Multiply the exponents in ${(b^{7})}^{3}$ .

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Step 7.1

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

$\frac{b^{7 \cdot 3}}{{(a^{5})}^{3} {(c^{2})}^{3}}$

Step 7.2

Multiply $7$ by $3$ .

$\frac{b^{21}}{{(a^{5})}^{3} {(c^{2})}^{3}}$

Step 8

Simplify the denominator.

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Step 8.1

Multiply the exponents in ${(a^{5})}^{3}$ .

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Step 8.1.1

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

$\frac{b^{21}}{a^{5 \cdot 3} {(c^{2})}^{3}}$

Step 8.1.2

Multiply $5$ by $3$ .

$\frac{b^{21}}{a^{15} {(c^{2})}^{3}}$

Step 8.2

Multiply the exponents in ${(c^{2})}^{3}$ .

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Step 8.2.1

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

$\frac{b^{21}}{a^{15} c^{2 \cdot 3}}$

Step 8.2.2

Multiply $2$ by $3$ .

$\frac{b^{21}}{a^{15} c^{6}}$