Algebra Examples

$(27 x y^{2} z^{2}) (- 3 x^{5} y^{3})$

Step 1

Multiply $x$ by $x^{5}$ by adding the exponents.

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Step 1.1

Move $x^{5}$ .

$27 (x^{5} x) y^{2} z^{2} (- 3 y^{3})$

Step 1.2

Multiply $x^{5}$ by $x$ .

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Step 1.2.1

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

$27 (x^{5} x^{1}) y^{2} z^{2} (- 3 y^{3})$

Step 1.2.2

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

$27 x^{5 + 1} y^{2} z^{2} (- 3 y^{3})$

Step 1.3

Add $5$ and $1$ .

$27 x^{6} y^{2} z^{2} (- 3 y^{3})$

Step 2

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

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Step 2.1

Move $y^{3}$ .

$27 x^{6} (y^{3} y^{2}) z^{2} \cdot - 3$

Step 2.2

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

$27 x^{6} y^{3 + 2} z^{2} \cdot - 3$

Step 2.3

Add $3$ and $2$ .

$27 x^{6} y^{5} z^{2} \cdot - 3$

Step 3

Multiply $- 3$ by $27$ .

$- 81 x^{6} y^{5} z^{2}$