Basic Math Examples

$(\frac{4}{5}) \cdot (- \frac{1}{3}) \cdot {(\frac{4}{5})}^{2} \cdot {(- \frac{1}{4})}^{4} \cdot (\frac{4}{5}) \cdot {(- \frac{1}{3})}^{0}$

Step 1

Multiply $\frac{4}{5}$ by ${(\frac{4}{5})}^{2}$ by adding the exponents.

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Step 1.1

Move ${(\frac{4}{5})}^{2}$ .

${(\frac{4}{5})}^{2} \frac{4}{5} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4} \cdot \frac{4}{5} \cdot {(- \frac{1}{3})}^{0}$

Step 1.2

Multiply ${(\frac{4}{5})}^{2}$ by $\frac{4}{5}$ .

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Step 1.2.1

Raise $\frac{4}{5}$ to the power of $1$ .

${(\frac{4}{5})}^{2} {(\frac{4}{5})}^{1} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4} \cdot \frac{4}{5} \cdot {(- \frac{1}{3})}^{0}$

Step 1.2.2

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

${(\frac{4}{5})}^{2 + 1} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4} \cdot \frac{4}{5} \cdot {(- \frac{1}{3})}^{0}$

Step 1.3

Add $2$ and $1$ .

${(\frac{4}{5})}^{3} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4} \cdot \frac{4}{5} \cdot {(- \frac{1}{3})}^{0}$

Step 2

Simplify ${(\frac{4}{5})}^{3} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4} \cdot \frac{4}{5} \cdot {(- \frac{1}{3})}^{0}$ .

${(\frac{4}{5})}^{3} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4} \cdot \frac{4}{5}$

Step 3

Multiply ${(\frac{4}{5})}^{3}$ by $\frac{4}{5}$ by adding the exponents.

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Step 3.1

Move $\frac{4}{5}$ .

$\frac{4}{5} {(\frac{4}{5})}^{3} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4}$

Step 3.2

Multiply $\frac{4}{5}$ by ${(\frac{4}{5})}^{3}$ .

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Step 3.2.1

Raise $\frac{4}{5}$ to the power of $1$ .

${(\frac{4}{5})}^{1} {(\frac{4}{5})}^{3} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4}$

Step 3.2.2

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

${(\frac{4}{5})}^{1 + 3} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4}$

Step 3.3

Add $1$ and $3$ .

${(\frac{4}{5})}^{4} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4}$

Step 4

Apply the product rule to $\frac{4}{5}$ .

$\frac{4^{4}}{5^{4}} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4}$

Step 5

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

$\frac{256}{5^{4}} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4}$

Step 6

Raise $5$ to the power of $4$ .

$\frac{256}{625} \cdot (- \frac{1}{3}) \cdot {(- \frac{1}{4})}^{4}$

Step 7

Multiply $\frac{256}{625} (- \frac{1}{3})$ .

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Step 7.1

Multiply $\frac{256}{625}$ by $\frac{1}{3}$ .

$- \frac{256}{625 \cdot 3} \cdot {(- \frac{1}{4})}^{4}$

Step 7.2

Multiply $625$ by $3$ .

$- \frac{256}{1875} \cdot {(- \frac{1}{4})}^{4}$

Step 8

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

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Step 8.1

Apply the product rule to $- \frac{1}{4}$ .

$- \frac{256}{1875} \cdot ({(- 1)}^{4} {(\frac{1}{4})}^{4})$

Step 8.2

Apply the product rule to $\frac{1}{4}$ .

$- \frac{256}{1875} \cdot ({(- 1)}^{4} \frac{1^{4}}{4^{4}})$

Step 9

Multiply $- 1$ by ${(- 1)}^{4}$ by adding the exponents.

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Step 9.1

Move ${(- 1)}^{4}$ .

${(- 1)}^{4} \cdot - 1 \frac{256}{1875} \cdot \frac{1^{4}}{4^{4}}$

Step 9.2

Multiply ${(- 1)}^{4}$ by $- 1$ .

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Step 9.2.1

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

${(- 1)}^{4} \cdot {(- 1)}^{1} \frac{256}{1875} \cdot \frac{1^{4}}{4^{4}}$

Step 9.2.2

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

${(- 1)}^{4 + 1} \frac{256}{1875} \cdot \frac{1^{4}}{4^{4}}$

Step 9.3

Add $4$ and $1$ .

${(- 1)}^{5} \frac{256}{1875} \cdot \frac{1^{4}}{4^{4}}$

Step 10

Simplify the expression.

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Step 10.1

One to any power is one.

${(- 1)}^{5} \frac{256}{1875} \cdot \frac{1}{4^{4}}$

Step 10.2

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

${(- 1)}^{5} \frac{256}{1875} \cdot \frac{1}{256}$

Step 10.3

Raise $- 1$ to the power of $5$ .

$- \frac{256}{1875} \cdot \frac{1}{256}$

Step 11

Cancel the common factor of $256$ .

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Step 11.1

Move the leading negative in $- \frac{256}{1875}$ into the numerator.

$\frac{- 256}{1875} \cdot \frac{1}{256}$

Step 11.2

Factor $256$ out of $- 256$ .

$\frac{256 (- 1)}{1875} \cdot \frac{1}{256}$

Step 11.3

Cancel the common factor.

$\frac{256 \cdot - 1}{1875} \cdot \frac{1}{256}$

Step 11.4

Rewrite the expression.

$\frac{- 1}{1875}$

Step 12

Move the negative in front of the fraction.

$- \frac{1}{1875}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{1875}$

Decimal Form:

$- 0.0005\overline{3}$