Basic Math Examples

$\frac{b^{\frac{2}{5}} b^{\frac{1}{5}}}{- b^{- \frac{2}{5}}}$

Step 1

Multiply $b^{\frac{2}{5}}$ by $b^{\frac{1}{5}}$ by adding the exponents.

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Step 1.1

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

$\frac{b^{\frac{2}{5} + \frac{1}{5}}}{- b^{- \frac{2}{5}}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{b^{\frac{2 + 1}{5}}}{- b^{- \frac{2}{5}}}$

Step 1.3

Add $2$ and $1$ .

$\frac{b^{\frac{3}{5}}}{- b^{- \frac{2}{5}}}$

Step 2

Move $b^{- \frac{2}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{b^{\frac{3}{5}} b^{\frac{2}{5}}}{- 1}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $b^{\frac{3}{5}}$ by $b^{\frac{2}{5}}$ by adding the exponents.

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Step 3.1.1

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

$\frac{b^{\frac{3}{5} + \frac{2}{5}}}{- 1}$

Step 3.1.2

Combine the numerators over the common denominator.

$\frac{b^{\frac{3 + 2}{5}}}{- 1}$

Step 3.1.3

Add $3$ and $2$ .

$\frac{b^{\frac{5}{5}}}{- 1}$

Step 3.1.4

Divide $5$ by $5$ .

$\frac{b^{1}}{- 1}$

Step 3.2

Simplify $b^{1}$ .

$\frac{b}{- 1}$

Step 4

Move the negative one from the denominator of $\frac{b}{- 1}$ .

$- 1 \cdot b$

Step 5

Rewrite $- 1 \cdot b$ as $- b$ .

$- b$