Basic Math Examples

(\frac{2}{3}) {(0.5)}^{- \frac{2}{3}} - \frac{2}{3} {(0.5)}^{- \frac{1}{3}}

$(\frac{2}{3}) {(0.5)}^{- \frac{2}{3}} - \frac{2}{3} {(0.5)}^{- \frac{1}{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{2}{3} \cdot \frac{1}{{0.5}^{\frac{2}{3}}} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}

$\frac{2}{3} \cdot \frac{1}{{0.5}^{\frac{2}{3}}} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}$

Step 1.2

Combine.

\frac{2 \cdot 1}{3 \cdot {0.5}^{\frac{2}{3}}} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}

$\frac{2 \cdot 1}{3 \cdot {0.5}^{\frac{2}{3}}} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}$

Step 1.3

Multiply

2

$2$ by

1

$1$ .

\frac{2}{3 \cdot {0.5}^{\frac{2}{3}}} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}

$\frac{2}{3 \cdot {0.5}^{\frac{2}{3}}} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}$

Step 1.4

Raise

0.5

$0.5$ to the power of

\frac{2}{3}

$\frac{2}{3}$ .

\frac{2}{3 \cdot 0.62996052} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}

$\frac{2}{3 \cdot 0.62996052} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}$

Step 1.5

Multiply

3

$3$ by

0.62996052

$0.62996052$ .

\frac{2}{1.88988157} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}

$\frac{2}{1.88988157} - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}$

Step 1.6

Divide

2

$2$ by

1.88988157

$1.88988157$ .

1.05826736 - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}

$1.05826736 - \frac{2}{3} \cdot {(0.5)}^{- \frac{1}{3}}$

Step 1.7

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

1.05826736 - \frac{2}{3} \cdot \frac{1}{{0.5}^{\frac{1}{3}}}

$1.05826736 - \frac{2}{3} \cdot \frac{1}{{0.5}^{\frac{1}{3}}}$

Step 1.8

Raise

0.5

$0.5$ to the power of

\frac{1}{3}

$\frac{1}{3}$ .

1.05826736 - \frac{2}{3} \cdot \frac{1}{0.79370052}

$1.05826736 - \frac{2}{3} \cdot \frac{1}{0.79370052}$

Step 1.9

Divide

1

$1$ by

0.79370052

$0.79370052$ .

1.05826736 - \frac{2}{3} \cdot 1.25992104

$1.05826736 - \frac{2}{3} \cdot 1.25992104$

Step 1.10

Multiply

- \frac{2}{3} \cdot 1.25992104

$- \frac{2}{3} \cdot 1.25992104$ .

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Step 1.10.1

Multiply

1.25992104

$1.25992104$ by

- 1

$- 1$ .

1.05826736 - 1.25992104 (\frac{2}{3})

$1.05826736 - 1.25992104 (\frac{2}{3})$

Step 1.10.2

Combine

- 1.25992104

$- 1.25992104$ and

\frac{2}{3}

$\frac{2}{3}$ .

1.05826736 + \frac{- 1.25992104 \cdot 2}{3}

$1.05826736 + \frac{- 1.25992104 \cdot 2}{3}$

Step 1.10.3

Multiply

- 1.25992104

$- 1.25992104$ by

2

$2$ .

1.05826736 + \frac{- 2.51984209}{3}

$1.05826736 + \frac{- 2.51984209}{3}$

1.05826736 + \frac{- 2.51984209}{3}

$1.05826736 + \frac{- 2.51984209}{3}$

Step 1.11

Divide

- 2.51984209

$- 2.51984209$ by

3

$3$ .

1.05826736 - 0.83994736

$1.05826736 - 0.83994736$

1.05826736 - 0.83994736

$1.05826736 - 0.83994736$

Step 2

Subtract

0.83994736

$0.83994736$ from

1.05826736

$1.05826736$ .

0.21832

$0.21832$