Basic Math Examples

$a^{\frac{1}{4}} \cdot b^{\frac{1}{2}} \cdot a \cdot b^{\frac{1}{2}}$

Step 1

Multiply $a^{\frac{1}{4}}$ by $a$ by adding the exponents.

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Step 1.1

Move $a$ .

$a \cdot a^{\frac{1}{4}} \cdot b^{\frac{1}{2}} \cdot b^{\frac{1}{2}}$

Step 1.2

Multiply $a$ by $a^{\frac{1}{4}}$ .

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Step 1.2.1

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

$a^{1} a^{\frac{1}{4}} \cdot b^{\frac{1}{2}} \cdot b^{\frac{1}{2}}$

Step 1.2.2

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

$a^{1 + \frac{1}{4}} \cdot b^{\frac{1}{2}} \cdot b^{\frac{1}{2}}$

Step 1.3

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

$a^{\frac{4}{4} + \frac{1}{4}} \cdot b^{\frac{1}{2}} \cdot b^{\frac{1}{2}}$

Step 1.4

Combine the numerators over the common denominator.

$a^{\frac{4 + 1}{4}} \cdot b^{\frac{1}{2}} \cdot b^{\frac{1}{2}}$

Step 1.5

Add $4$ and $1$ .

$a^{\frac{5}{4}} \cdot b^{\frac{1}{2}} \cdot b^{\frac{1}{2}}$

Step 2

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

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Step 2.1

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

$a^{\frac{5}{4}} \cdot (b^{\frac{1}{2}} b^{\frac{1}{2}})$

Step 2.2

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

$a^{\frac{5}{4}} \cdot b^{\frac{1}{2} + \frac{1}{2}}$

Step 2.3

Combine the numerators over the common denominator.

$a^{\frac{5}{4}} \cdot b^{\frac{1 + 1}{2}}$

Step 2.4

Add $1$ and $1$ .

$a^{\frac{5}{4}} \cdot b^{\frac{2}{2}}$

Step 2.5

Divide $2$ by $2$ .

$a^{\frac{5}{4}} \cdot b^{1}$

Step 3

Simplify $a^{\frac{5}{4}} \cdot b^{1}$ .

$a^{\frac{5}{4}} \cdot b$

Step 4

Reorder factors in $a^{\frac{5}{4}} b$ .

$b a^{\frac{5}{4}}$