Basic Math Examples

${(8 a^{3} b^{- 5} c^{- 2})}^{2}$

Step 1

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

${(8 a^{3} \frac{1}{b^{5}} c^{- 2})}^{2}$

Step 2

Multiply $8 a^{3} \frac{1}{b^{5}}$ .

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Step 2.1

Combine $8$ and $\frac{1}{b^{5}}$ .

${(a^{3} \frac{8}{b^{5}} c^{- 2})}^{2}$

Step 2.2

Combine $a^{3}$ and $\frac{8}{b^{5}}$ .

${(\frac{a^{3} \cdot 8}{b^{5}} c^{- 2})}^{2}$

Step 3

Move $8$ to the left of $a^{3}$ .

${(\frac{8 \cdot a^{3}}{b^{5}} c^{- 2})}^{2}$

Step 4

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

${(\frac{8 a^{3}}{b^{5}} \cdot \frac{1}{c^{2}})}^{2}$

Step 5

Combine.

${(\frac{8 a^{3} \cdot 1}{b^{5} c^{2}})}^{2}$

Step 6

Multiply $8$ by $1$ .

${(\frac{8 a^{3}}{b^{5} c^{2}})}^{2}$

Step 7

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

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Step 7.1

Apply the product rule to $\frac{8 a^{3}}{b^{5} c^{2}}$ .

$\frac{{(8 a^{3})}^{2}}{{(b^{5} c^{2})}^{2}}$

Step 7.2

Apply the product rule to $8 a^{3}$ .

$\frac{8^{2} {(a^{3})}^{2}}{{(b^{5} c^{2})}^{2}}$

Step 7.3

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

$\frac{8^{2} {(a^{3})}^{2}}{{(b^{5})}^{2} {(c^{2})}^{2}}$

Step 8

Simplify the numerator.

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Step 8.1

Raise $8$ to the power of $2$ .

$\frac{64 {(a^{3})}^{2}}{{(b^{5})}^{2} {(c^{2})}^{2}}$

Step 8.2

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

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Step 8.2.1

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

$\frac{64 a^{3 \cdot 2}}{{(b^{5})}^{2} {(c^{2})}^{2}}$

Step 8.2.2

Multiply $3$ by $2$ .

$\frac{64 a^{6}}{{(b^{5})}^{2} {(c^{2})}^{2}}$

Step 9

Simplify the denominator.

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Step 9.1

Multiply the exponents in ${(b^{5})}^{2}$ .

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Step 9.1.1

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

$\frac{64 a^{6}}{b^{5 \cdot 2} {(c^{2})}^{2}}$

Step 9.1.2

Multiply $5$ by $2$ .

$\frac{64 a^{6}}{b^{10} {(c^{2})}^{2}}$

Step 9.2

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

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Step 9.2.1

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

$\frac{64 a^{6}}{b^{10} c^{2 \cdot 2}}$

Step 9.2.2

Multiply $2$ by $2$ .

$\frac{64 a^{6}}{b^{10} c^{4}}$