Basic Math Examples

$5 h^{\frac{3}{2}} (h^{- 2}) (h^{\frac{1}{2}})$

Step 1

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

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Step 1.1

Move $h^{- 2}$ .

$5 (h^{- 2} h^{\frac{3}{2}}) h^{\frac{1}{2}}$

Step 1.2

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

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

Step 1.3

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.4

Combine $- 2$ and $\frac{2}{2}$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 2$ by $2$ .

$5 h^{\frac{- 4 + 3}{2}} h^{\frac{1}{2}}$

Step 1.6.2

Add $- 4$ and $3$ .

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

Step 1.7

Move the negative in front of the fraction.

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

Step 2

Multiply $h^{- \frac{1}{2}}$ by $h^{\frac{1}{2}}$ by adding the exponents.

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Step 2.1

Move $h^{\frac{1}{2}}$ .

$5 (h^{\frac{1}{2}} h^{- \frac{1}{2}})$

Step 2.2

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

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Subtract $1$ from $1$ .

$5 h^{\frac{0}{2}}$

Step 2.5

Divide $0$ by $2$ .

$5 h^{0}$

Step 3

Simplify $5 h^{0}$ .

$5$