Basic Math Examples

$\frac{{(2 b^{- 7} c^{4})}^{4}}{5^{- 1} b^{2} c^{6}}$

Step 1

Move $5^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(2 b^{- 7} c^{4})}^{4} \cdot 5}{b^{2} c^{6}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $2 b^{- 7} c^{4}$ .

$\frac{{(2 b^{- 7})}^{4} {(c^{4})}^{4} \cdot 5}{b^{2} c^{6}}$

Step 2.2

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

$\frac{{(2 \frac{1}{b^{7}})}^{4} {(c^{4})}^{4} \cdot 5}{b^{2} c^{6}}$

Step 2.3

Combine $2$ and $\frac{1}{b^{7}}$ .

$\frac{{(\frac{2}{b^{7}})}^{4} {(c^{4})}^{4} \cdot 5}{b^{2} c^{6}}$

Step 2.4

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

$\frac{\frac{2^{4}}{{(b^{7})}^{4}} {(c^{4})}^{4} \cdot 5}{b^{2} c^{6}}$

Step 2.5

Raise $2$ to the power of $4$ .

$\frac{\frac{16}{{(b^{7})}^{4}} {(c^{4})}^{4} \cdot 5}{b^{2} c^{6}}$

Step 2.6

Multiply the exponents in ${(b^{7})}^{4}$ .

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Step 2.6.1

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

$\frac{\frac{16}{b^{7 \cdot 4}} {(c^{4})}^{4} \cdot 5}{b^{2} c^{6}}$

Step 2.6.2

Multiply $7$ by $4$ .

$\frac{\frac{16}{b^{28}} {(c^{4})}^{4} \cdot 5}{b^{2} c^{6}}$

Step 2.7

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

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Step 2.7.1

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

$\frac{\frac{16}{b^{28}} c^{4 \cdot 4} \cdot 5}{b^{2} c^{6}}$

Step 2.7.2

Multiply $4$ by $4$ .

$\frac{\frac{16}{b^{28}} c^{16} \cdot 5}{b^{2} c^{6}}$

Step 2.8

Combine exponents.

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Step 2.8.1

Combine $\frac{16}{b^{28}}$ and $c^{16}$ .

$\frac{\frac{16 c^{16}}{b^{28}} \cdot 5}{b^{2} c^{6}}$

Step 2.8.2

Combine $\frac{16 c^{16}}{b^{28}}$ and $5$ .

$\frac{\frac{16 c^{16} \cdot 5}{b^{28}}}{b^{2} c^{6}}$

Step 2.8.3

Multiply $5$ by $16$ .

$\frac{\frac{80 c^{16}}{b^{28}}}{b^{2} c^{6}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{80 c^{16}}{b^{28}} \cdot \frac{1}{b^{2} c^{6}}$

Step 4

Combine.

$\frac{80 c^{16} \cdot 1}{b^{28} (b^{2} c^{6})}$

Step 5

Multiply $b^{28}$ by $b^{2}$ by adding the exponents.

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Step 5.1

Move $b^{2}$ .

$\frac{80 c^{16} \cdot 1}{b^{2} b^{28} c^{6}}$

Step 5.2

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

$\frac{80 c^{16} \cdot 1}{b^{2 + 28} c^{6}}$

Step 5.3

Add $2$ and $28$ .

$\frac{80 c^{16} \cdot 1}{b^{30} c^{6}}$

Step 6

Multiply $80 c^{16}$ by $1$ .

$\frac{80 c^{16}}{b^{30} c^{6}}$

Step 7

Cancel the common factor of $c^{16}$ and $c^{6}$ .

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Step 7.1

Factor $c^{6}$ out of $80 c^{16}$ .

$\frac{c^{6} (80 c^{10})}{b^{30} c^{6}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $c^{6}$ out of $b^{30} c^{6}$ .

$\frac{c^{6} (80 c^{10})}{c^{6} b^{30}}$

Step 7.2.2

Cancel the common factor.

$\frac{c^{6} (80 c^{10})}{c^{6} b^{30}}$

Step 7.2.3

Rewrite the expression.

$\frac{80 c^{10}}{b^{30}}$