Basic Math Examples

${(- \frac{3}{5} - \frac{5}{8})}^{4}$

Step 1

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

${(- \frac{3}{5} \cdot \frac{8}{8} - \frac{5}{8})}^{4}$

Step 2

To write $- \frac{5}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

${(- \frac{3}{5} \cdot \frac{8}{8} - \frac{5}{8} \cdot \frac{5}{5})}^{4}$

Step 3

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{5}$ by $\frac{8}{8}$ .

${(- \frac{3 \cdot 8}{5 \cdot 8} - \frac{5}{8} \cdot \frac{5}{5})}^{4}$

Step 3.2

Multiply $5$ by $8$ .

${(- \frac{3 \cdot 8}{40} - \frac{5}{8} \cdot \frac{5}{5})}^{4}$

Step 3.3

Multiply $\frac{5}{8}$ by $\frac{5}{5}$ .

${(- \frac{3 \cdot 8}{40} - \frac{5 \cdot 5}{8 \cdot 5})}^{4}$

Step 3.4

Multiply $8$ by $5$ .

${(- \frac{3 \cdot 8}{40} - \frac{5 \cdot 5}{40})}^{4}$

Step 4

Combine the numerators over the common denominator.

${(\frac{- 3 \cdot 8 - 5 \cdot 5}{40})}^{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 3$ by $8$ .

${(\frac{- 24 - 5 \cdot 5}{40})}^{4}$

Step 5.2

Multiply $- 5$ by $5$ .

${(\frac{- 24 - 25}{40})}^{4}$

Step 5.3

Subtract $25$ from $- 24$ .

${(\frac{- 49}{40})}^{4}$

Step 6

Move the negative in front of the fraction.

${(- \frac{49}{40})}^{4}$

Step 7

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

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Step 7.1

Apply the product rule to $- \frac{49}{40}$ .

${(- 1)}^{4} {(\frac{49}{40})}^{4}$

Step 7.2

Apply the product rule to $\frac{49}{40}$ .

${(- 1)}^{4} \frac{49^{4}}{40^{4}}$

Step 8

Raise $- 1$ to the power of $4$ .

$1 \frac{49^{4}}{40^{4}}$

Step 9

Multiply $\frac{49^{4}}{40^{4}}$ by $1$ .

$\frac{49^{4}}{40^{4}}$

Step 10

Raise $49$ to the power of $4$ .

$\frac{5764801}{40^{4}}$

Step 11

Raise $40$ to the power of $4$ .

$\frac{5764801}{2560000}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{5764801}{2560000}$

Decimal Form:

$2.25187539 \dots$

Mixed Number Form:

$2 \frac{644801}{2560000}$