Basic Math Examples

${(\frac{a^{3} b^{- 2} c^{- 4}}{b^{- 1} c})}^{5}$

Step 1

Move $b^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{a^{3} c^{- 4}}{b^{- 1} c b^{2}})}^{5}$

Step 2

Move $c^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{a^{3}}{b^{- 1} c b^{2} c^{4}})}^{5}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $b^{- 1}$ by $b^{2}$ by adding the exponents.

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Step 3.1.1

Move $b^{2}$ .

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

Step 3.1.2

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

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

Step 3.1.3

Subtract $1$ from $2$ .

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

Step 3.2

Simplify $b^{1} c$ .

${(\frac{a^{3}}{b c \cdot c^{4}})}^{5}$

Step 3.3

Multiply $c$ by $c^{4}$ by adding the exponents.

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Step 3.3.1

Move $c^{4}$ .

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

Step 3.3.2

Multiply $c^{4}$ by $c$ .

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Step 3.3.2.1

Raise $c$ to the power of $1$ .

${(\frac{a^{3}}{b (c^{4} c^{1})})}^{5}$

Step 3.3.2.2

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

${(\frac{a^{3}}{b c^{4 + 1}})}^{5}$

Step 3.3.3

Add $4$ and $1$ .

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

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 $\frac{a^{3}}{b c^{5}}$ .

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

Step 4.2

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $3$ by $5$ .

$\frac{a^{15}}{b^{5} {(c^{5})}^{5}}$

Step 6

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

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Step 6.1

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

$\frac{a^{15}}{b^{5} c^{5 \cdot 5}}$

Step 6.2

Multiply $5$ by $5$ .

$\frac{a^{15}}{b^{5} c^{25}}$