Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

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

Step 1.2

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

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

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

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

Step 1.4

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

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

Step 1.5

Multiply $\frac{3}{4}$ by $1$ .

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

Step 1.6

Multiply $- 1$ by ${(- 1)}^{\frac{5}{3}}$ by adding the exponents.

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Step 1.6.1

Move ${(- 1)}^{\frac{5}{3}}$ .

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

Step 1.6.2

Multiply ${(- 1)}^{\frac{5}{3}}$ by $- 1$ .

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Step 1.6.2.1

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

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

Step 1.6.2.2

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

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

Step 1.6.3

Write $1$ as a fraction with a common denominator.

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

Step 1.6.4

Combine the numerators over the common denominator.

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

Step 1.6.5

Add $5$ and $3$ .

$\frac{3}{4} + {(- 1)}^{\frac{8}{3}} \frac{3}{5}$

Step 1.7

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$\frac{3}{4} + {({(- 1)}^{3})}^{\frac{8}{3}} \frac{3}{5}$

Step 1.8

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

$\frac{3}{4} + {(- 1)}^{3 (\frac{8}{3})} \frac{3}{5}$

Step 1.9

Cancel the common factor of $3$ .

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Step 1.9.1

Cancel the common factor.

$\frac{3}{4} + {(- 1)}^{3 (\frac{8}{3})} \frac{3}{5}$

Step 1.9.2

Rewrite the expression.

$\frac{3}{4} + {(- 1)}^{8} \frac{3}{5}$

Step 1.10

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

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

Step 1.11

Multiply $\frac{3}{5}$ by $1$ .

$\frac{3}{4} + \frac{3}{5}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3}{4} \cdot \frac{5}{5} + \frac{3}{5}$

Step 3

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{4} \cdot \frac{5}{5} + \frac{3}{5} \cdot \frac{4}{4}$

Step 4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{4}$ by $\frac{5}{5}$ .

$\frac{3 \cdot 5}{4 \cdot 5} + \frac{3}{5} \cdot \frac{4}{4}$

Step 4.2

Multiply $4$ by $5$ .

$\frac{3 \cdot 5}{20} + \frac{3}{5} \cdot \frac{4}{4}$

Step 4.3

Multiply $\frac{3}{5}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 5}{20} + \frac{3 \cdot 4}{5 \cdot 4}$

Step 4.4

Multiply $5$ by $4$ .

$\frac{3 \cdot 5}{20} + \frac{3 \cdot 4}{20}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 5 + 3 \cdot 4}{20}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $5$ .

$\frac{15 + 3 \cdot 4}{20}$

Step 6.2

Multiply $3$ by $4$ .

$\frac{15 + 12}{20}$

Step 6.3

Add $15$ and $12$ .

$\frac{27}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{20}$

Decimal Form:

$1.35$

Mixed Number Form:

$1 \frac{7}{20}$