Algebra Examples

$8 x^{8} y^{6} z \cdot 5 x^{5} y^{3} z^{2} \cdot 4 x^{3} y^{4} z^{2}$

Step 1

Multiply $x^{8}$ by $x^{5}$ by adding the exponents.

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Step 1.1

Move $x^{5}$ .

$8 (x^{5} x^{8}) y^{6} z \cdot (5 y^{3} z^{2}) \cdot (4 x^{3} y^{4} z^{2})$

Step 1.2

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

$8 x^{5 + 8} y^{6} z \cdot (5 y^{3} z^{2}) \cdot (4 x^{3} y^{4} z^{2})$

Step 1.3

Add $5$ and $8$ .

$8 x^{13} y^{6} z \cdot (5 y^{3} z^{2}) \cdot (4 x^{3} y^{4} z^{2})$

Step 2

Multiply $x^{13}$ by $x^{3}$ by adding the exponents.

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Step 2.1

Move $x^{3}$ .

$8 (x^{3} x^{13}) y^{6} z \cdot (5 y^{3} z^{2}) \cdot (4 y^{4} z^{2})$

Step 2.2

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

$8 x^{3 + 13} y^{6} z \cdot (5 y^{3} z^{2}) \cdot (4 y^{4} z^{2})$

Step 2.3

Add $3$ and $13$ .

$8 x^{16} y^{6} z \cdot (5 y^{3} z^{2}) \cdot (4 y^{4} z^{2})$

Step 3

Multiply $y^{6}$ by $y^{3}$ by adding the exponents.

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Step 3.1

Move $y^{3}$ .

$8 x^{16} (y^{3} y^{6}) z \cdot (5 z^{2}) \cdot (4 y^{4} z^{2})$

Step 3.2

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

$8 x^{16} y^{3 + 6} z \cdot (5 z^{2}) \cdot (4 y^{4} z^{2})$

Step 3.3

Add $3$ and $6$ .

$8 x^{16} y^{9} z \cdot (5 z^{2}) \cdot (4 y^{4} z^{2})$

Step 4

Multiply $y^{9}$ by $y^{4}$ by adding the exponents.

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Step 4.1

Move $y^{4}$ .

$8 x^{16} (y^{4} y^{9}) z \cdot (5 z^{2}) \cdot (4 z^{2})$

Step 4.2

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

$8 x^{16} y^{4 + 9} z \cdot (5 z^{2}) \cdot (4 z^{2})$

Step 4.3

Add $4$ and $9$ .

$8 x^{16} y^{13} z \cdot (5 z^{2}) \cdot (4 z^{2})$

Step 5

Multiply $z$ by $z^{2}$ by adding the exponents.

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Step 5.1

Move $z^{2}$ .

$8 x^{16} y^{13} (z^{2} z) \cdot 5 \cdot (4 z^{2})$

Step 5.2

Multiply $z^{2}$ by $z$ .

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Step 5.2.1

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

$8 x^{16} y^{13} (z^{2} z^{1}) \cdot 5 \cdot (4 z^{2})$

Step 5.2.2

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

$8 x^{16} y^{13} z^{2 + 1} \cdot 5 \cdot (4 z^{2})$

Step 5.3

Add $2$ and $1$ .

$8 x^{16} y^{13} z^{3} \cdot 5 \cdot (4 z^{2})$

Step 6

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

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Step 6.1

Move $z^{2}$ .

$8 x^{16} y^{13} (z^{2} z^{3}) \cdot 5 \cdot 4$

Step 6.2

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

$8 x^{16} y^{13} z^{2 + 3} \cdot 5 \cdot 4$

Step 6.3

Add $2$ and $3$ .

$8 x^{16} y^{13} z^{5} \cdot 5 \cdot 4$

Step 7

Multiply $5$ by $8$ .

$40 x^{16} y^{13} z^{5} \cdot 4$

Step 8

Multiply $4$ by $40$ .

$160 x^{16} y^{13} z^{5}$