Algebra Examples

(10 x^{3} y z^{2}) (- 2 x y^{5} z)

$(10 x^{3} y z^{2}) (- 2 x y^{5} z)$

Step 1

Multiply

x^{3}

$x^{3}$ by

x

$x$ by adding the exponents.

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Step 1.1

Move

x

$x$ .

10 (x \cdot x^{3}) y z^{2} (- 2 y^{5} z)

$10 (x \cdot x^{3}) y z^{2} (- 2 y^{5} z)$

Step 1.2

Multiply

x

$x$ by

x^{3}

$x^{3}$ .

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Step 1.2.1

Raise

x

$x$ to the power of

1

$1$ .

10 (x^{1} x^{3}) y z^{2} (- 2 y^{5} z)

$10 (x^{1} x^{3}) y z^{2} (- 2 y^{5} z)$

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.

10 x^{1 + 3} y z^{2} (- 2 y^{5} z)

$10 x^{1 + 3} y z^{2} (- 2 y^{5} z)$

10 x^{1 + 3} y z^{2} (- 2 y^{5} z)

$10 x^{1 + 3} y z^{2} (- 2 y^{5} z)$

Step 1.3

Add

1

$1$ and

3

$3$ .

10 x^{4} y z^{2} (- 2 y^{5} z)

$10 x^{4} y z^{2} (- 2 y^{5} z)$

10 x^{4} y z^{2} (- 2 y^{5} z)

$10 x^{4} y z^{2} (- 2 y^{5} z)$

Step 2

Multiply

y

$y$ by

y^{5}

$y^{5}$ by adding the exponents.

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Step 2.1

Move

y^{5}

$y^{5}$ .

10 x^{4} (y^{5} y) z^{2} (- 2 z)

$10 x^{4} (y^{5} y) z^{2} (- 2 z)$

Step 2.2

Multiply

y^{5}

$y^{5}$ by

y

$y$ .

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Step 2.2.1

Raise

y

$y$ to the power of

1

$1$ .

10 x^{4} (y^{5} y^{1}) z^{2} (- 2 z)

$10 x^{4} (y^{5} y^{1}) z^{2} (- 2 z)$

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.

10 x^{4} y^{5 + 1} z^{2} (- 2 z)

$10 x^{4} y^{5 + 1} z^{2} (- 2 z)$

10 x^{4} y^{5 + 1} z^{2} (- 2 z)

$10 x^{4} y^{5 + 1} z^{2} (- 2 z)$

Step 2.3

Add

5

$5$ and

1

$1$ .

10 x^{4} y^{6} z^{2} (- 2 z)

$10 x^{4} y^{6} z^{2} (- 2 z)$

10 x^{4} y^{6} z^{2} (- 2 z)

$10 x^{4} y^{6} z^{2} (- 2 z)$

Step 3

Multiply

z^{2}

$z^{2}$ by

z

$z$ by adding the exponents.

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Step 3.1

Move

z

$z$ .

10 x^{4} y^{6} (z \cdot z^{2}) \cdot - 2

$10 x^{4} y^{6} (z \cdot z^{2}) \cdot - 2$

Step 3.2

Multiply

z

$z$ by

z^{2}

$z^{2}$ .

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Step 3.2.1

Raise

z

$z$ to the power of

1

$1$ .

10 x^{4} y^{6} (z^{1} z^{2}) \cdot - 2

$10 x^{4} y^{6} (z^{1} z^{2}) \cdot - 2$

Step 3.2.2

Use the power rule

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

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

10 x^{4} y^{6} z^{1 + 2} \cdot - 2

$10 x^{4} y^{6} z^{1 + 2} \cdot - 2$

10 x^{4} y^{6} z^{1 + 2} \cdot - 2

$10 x^{4} y^{6} z^{1 + 2} \cdot - 2$

Step 3.3

Add

1

$1$ and

2

$2$ .

10 x^{4} y^{6} z^{3} \cdot - 2

$10 x^{4} y^{6} z^{3} \cdot - 2$

10 x^{4} y^{6} z^{3} \cdot - 2

$10 x^{4} y^{6} z^{3} \cdot - 2$

Step 4

Multiply

- 2

$- 2$ by

10

$10$ .

- 20 x^{4} y^{6} z^{3}

$- 20 x^{4} y^{6} z^{3}$

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

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