Algebra Examples

$7 x^{2} y^{10} z^{5} \cdot 12 x^{5} y^{0} z$

Step 1

Multiply $x^{2}$ by $x^{5}$ by adding the exponents.

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Step 1.1

Move $x^{5}$ .

$7 (x^{5} x^{2}) y^{10} z^{5} \cdot (12 y^{0} z)$

Step 1.2

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

$7 x^{5 + 2} y^{10} z^{5} \cdot (12 y^{0} z)$

Step 1.3

Add $5$ and $2$ .

$7 x^{7} y^{10} z^{5} \cdot (12 y^{0} z)$

Step 2

Simplify $7 x^{7} y^{10} z^{5} \cdot (12 y^{0} z)$ .

$7 x^{7} y^{10} z^{5} \cdot (12 z)$

Step 3

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

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Step 3.1

Move $z$ .

$7 x^{7} y^{10} (z \cdot z^{5}) \cdot 12$

Step 3.2

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

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Step 3.2.1

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

$7 x^{7} y^{10} (z^{1} z^{5}) \cdot 12$

Step 3.2.2

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

$7 x^{7} y^{10} z^{1 + 5} \cdot 12$

Step 3.3

Add $1$ and $5$ .

$7 x^{7} y^{10} z^{6} \cdot 12$

Step 4

Multiply $12$ by $7$ .

$84 x^{7} y^{10} z^{6}$