Algebra Examples

${(\frac{5 a^{0} b^{4}}{c^{- 3}})}^{2}$

Step 1

Move $c^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(5 a^{0} b^{4} c^{3})}^{2}$

Step 2

Anything raised to $0$ is $1$ .

${(5 \cdot 1 b^{4} c^{3})}^{2}$

Step 3

Multiply $5$ by $1$ .

${(5 b^{4} c^{3})}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $5 b^{4} c^{3}$ .

${(5 b^{4})}^{2} {(c^{3})}^{2}$

Step 4.2

Apply the product rule to $5 b^{4}$ .

$5^{2} {(b^{4})}^{2} {(c^{3})}^{2}$

Step 5

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

$25 {(b^{4})}^{2} {(c^{3})}^{2}$

Step 6

Multiply the exponents in ${(b^{4})}^{2}$ .

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Step 6.1

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

$25 b^{4 \cdot 2} {(c^{3})}^{2}$

Step 6.2

Multiply $4$ by $2$ .

$25 b^{8} {(c^{3})}^{2}$

Step 7

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

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Step 7.1

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

$25 b^{8} c^{3 \cdot 2}$

Step 7.2

Multiply $3$ by $2$ .

$25 b^{8} c^{6}$