Basic Math Examples

${(\frac{- 4}{7})}^{8} \div {(\frac{- 4}{7})}^{0}$

Step 1

Rewrite the division as a fraction.

$\frac{{(\frac{- 4}{7})}^{8}}{{(\frac{- 4}{7})}^{0}}$

Step 2

Cancel the common factor of ${(\frac{- 4}{7})}^{8}$ and ${(\frac{- 4}{7})}^{0}$ .

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Step 2.1

Factor ${(\frac{- 4}{7})}^{0}$ out of ${(\frac{- 4}{7})}^{8}$ .

$\frac{{(\frac{- 4}{7})}^{0} {(\frac{- 4}{7})}^{8}}{{(\frac{- 4}{7})}^{0}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{{(\frac{- 4}{7})}^{0} {(\frac{- 4}{7})}^{8}}{{(\frac{- 4}{7})}^{0} \cdot 1}$

Step 2.2.2

Cancel the common factor.

$\frac{{(\frac{- 4}{7})}^{0} {(\frac{- 4}{7})}^{8}}{{(\frac{- 4}{7})}^{0} \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{{(\frac{- 4}{7})}^{8}}{1}$

Step 2.2.4

Divide ${(\frac{- 4}{7})}^{8}$ by $1$ .

${(\frac{- 4}{7})}^{8}$

Step 3

Move the negative in front of the fraction.

${(- \frac{4}{7})}^{8}$

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 $- \frac{4}{7}$ .

${(- 1)}^{8} {(\frac{4}{7})}^{8}$

Step 4.2

Apply the product rule to $\frac{4}{7}$ .

${(- 1)}^{8} \frac{4^{8}}{7^{8}}$

Step 5

Raise $- 1$ to the power of $8$ .

$1 \frac{4^{8}}{7^{8}}$

Step 6

Multiply $\frac{4^{8}}{7^{8}}$ by $1$ .

$\frac{4^{8}}{7^{8}}$

Step 7

Raise $4$ to the power of $8$ .

$\frac{65536}{7^{8}}$

Step 8

Raise $7$ to the power of $8$ .

$\frac{65536}{5764801}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{65536}{5764801}$

Decimal Form:

$0.01136830 \dots$