Algebra Examples

(a b^{2}) (a^{2} b)

$(a b^{2}) (a^{2} b)$

Step 1

Multiply

a

$a$ by

a^{2}

$a^{2}$ by adding the exponents.

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Step 1.1

Move

a^{2}

$a^{2}$ .

a^{2} a b^{2} b

$a^{2} a b^{2} b$

Step 1.2

Multiply

a^{2}

$a^{2}$ by

a

$a$ .

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Step 1.2.1

Raise

a

$a$ to the power of

1

$1$ .

a^{2} a^{1} b^{2} b

$a^{2} a^{1} b^{2} b$

Step 1.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

a^{2 + 1} b^{2} b

$a^{2 + 1} b^{2} b$

a^{2 + 1} b^{2} b

$a^{2 + 1} b^{2} b$

Step 1.3

Add

2

$2$ and

1

$1$ .

a^{3} b^{2} b

$a^{3} b^{2} b$

a^{3} b^{2} b

$a^{3} b^{2} b$

Step 2

Multiply

b^{2}

$b^{2}$ by

b

$b$ by adding the exponents.

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Step 2.1

Move

b

$b$ .

a^{3} (b \cdot b^{2})

$a^{3} (b \cdot b^{2})$

Step 2.2

Multiply

b

$b$ by

b^{2}

$b^{2}$ .

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Step 2.2.1

Raise

b

$b$ to the power of

1

$1$ .

a^{3} (b^{1} b^{2})

$a^{3} (b^{1} b^{2})$

Step 2.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

a^{3} b^{1 + 2}

$a^{3} b^{1 + 2}$

a^{3} b^{1 + 2}

$a^{3} b^{1 + 2}$

Step 2.3

Add

1

$1$ and

2

$2$ .

a^{3} b^{3}

$a^{3} b^{3}$

a^{3} b^{3}

$a^{3} b^{3}$

(a b^{2}) (a^{2} b)

$(a b^{2}) (a^{2} b)$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$