Basic Math Examples

$\frac{10}{3} \cdot {(3)}^{\frac{2}{3}} - \frac{20}{3} \cdot {(3)}^{\frac{1}{3}}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{10}{3}$ and $3^{\frac{2}{3}}$ .

$\frac{10 \cdot 3^{\frac{2}{3}}}{3} - \frac{20}{3} \cdot {(3)}^{\frac{1}{3}}$

Step 1.2

Move $3^{\frac{2}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{10}{3 \cdot 3^{- \frac{2}{3}}} - \frac{20}{3} \cdot {(3)}^{\frac{1}{3}}$

Step 1.3

Multiply $3$ by $3^{- \frac{2}{3}}$ by adding the exponents.

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Step 1.3.1

Multiply $3$ by $3^{- \frac{2}{3}}$ .

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Step 1.3.1.1

Raise $3$ to the power of $1$ .

$\frac{10}{3^{1} \cdot 3^{- \frac{2}{3}}} - \frac{20}{3} \cdot {(3)}^{\frac{1}{3}}$

Step 1.3.1.2

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

$\frac{10}{3^{1 - \frac{2}{3}}} - \frac{20}{3} \cdot {(3)}^{\frac{1}{3}}$

Step 1.3.2

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

$\frac{10}{3^{\frac{3}{3} - \frac{2}{3}}} - \frac{20}{3} \cdot {(3)}^{\frac{1}{3}}$

Step 1.3.3

Combine the numerators over the common denominator.

$\frac{10}{3^{\frac{3 - 2}{3}}} - \frac{20}{3} \cdot {(3)}^{\frac{1}{3}}$

Step 1.3.4

Subtract $2$ from $3$ .

$\frac{10}{3^{\frac{1}{3}}} - \frac{20}{3} \cdot {(3)}^{\frac{1}{3}}$

Step 1.4

Combine $3^{\frac{1}{3}}$ and $\frac{20}{3}$ .

$\frac{10}{3^{\frac{1}{3}}} - \frac{3^{\frac{1}{3}} \cdot 20}{3}$

Step 1.5

Move $3^{\frac{1}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{10}{3^{\frac{1}{3}}} - \frac{20}{3 \cdot 3^{- \frac{1}{3}}}$

Step 1.6

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

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Step 1.6.1

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

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Step 1.6.1.1

Raise $3$ to the power of $1$ .

$\frac{10}{3^{\frac{1}{3}}} - \frac{20}{3^{1} \cdot 3^{- \frac{1}{3}}}$

Step 1.6.1.2

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

$\frac{10}{3^{\frac{1}{3}}} - \frac{20}{3^{1 - \frac{1}{3}}}$

Step 1.6.2

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

$\frac{10}{3^{\frac{1}{3}}} - \frac{20}{3^{\frac{3}{3} - \frac{1}{3}}}$

Step 1.6.3

Combine the numerators over the common denominator.

$\frac{10}{3^{\frac{1}{3}}} - \frac{20}{3^{\frac{3 - 1}{3}}}$

Step 1.6.4

Subtract $1$ from $3$ .

$\frac{10}{3^{\frac{1}{3}}} - \frac{20}{3^{\frac{2}{3}}}$

Step 2

To write $\frac{10}{3^{\frac{1}{3}}}$ as a fraction with a common denominator, multiply by $\frac{3^{\frac{1}{3}}}{3^{\frac{1}{3}}}$ .

$\frac{10}{3^{\frac{1}{3}}} \cdot \frac{3^{\frac{1}{3}}}{3^{\frac{1}{3}}} - \frac{20}{3^{\frac{2}{3}}}$

Step 3

Write each expression with a common denominator of $3^{\frac{2}{3}}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{10}{3^{\frac{1}{3}}}$ by $\frac{3^{\frac{1}{3}}}{3^{\frac{1}{3}}}$ .

$\frac{10 \cdot 3^{\frac{1}{3}}}{3^{\frac{1}{3}} \cdot 3^{\frac{1}{3}}} - \frac{20}{3^{\frac{2}{3}}}$

Step 3.2

Multiply $3^{\frac{1}{3}}$ by $3^{\frac{1}{3}}$ by adding the exponents.

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Step 3.2.1

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

$\frac{10 \cdot 3^{\frac{1}{3}}}{3^{\frac{1}{3} + \frac{1}{3}}} - \frac{20}{3^{\frac{2}{3}}}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{10 \cdot 3^{\frac{1}{3}}}{3^{\frac{1 + 1}{3}}} - \frac{20}{3^{\frac{2}{3}}}$

Step 3.2.3

Add $1$ and $1$ .

$\frac{10 \cdot 3^{\frac{1}{3}}}{3^{\frac{2}{3}}} - \frac{20}{3^{\frac{2}{3}}}$

Step 4

Combine the numerators over the common denominator.

$\frac{10 \cdot 3^{\frac{1}{3}} - 20}{3^{\frac{2}{3}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{10 \cdot 3^{\frac{1}{3}} - 20}{3^{\frac{2}{3}}}$

Decimal Form:

$- 2.68138439 \dots$