Algebra Examples

$(8 x^{\frac{1}{7}} y^{\frac{3}{12}}) (2 y^{\frac{8}{12}} z^{2}) (4 x^{\frac{3}{7}} z^{4})$

Step 1

Multiply $x^{\frac{1}{7}}$ by $x^{\frac{3}{7}}$ by adding the exponents.

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Step 1.1

Move $x^{\frac{3}{7}}$ .

$8 (x^{\frac{3}{7}} x^{\frac{1}{7}}) y^{\frac{3}{12}} (2 y^{\frac{8}{12}} z^{2}) (4 z^{4})$

Step 1.2

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

$8 x^{\frac{3}{7} + \frac{1}{7}} y^{\frac{3}{12}} (2 y^{\frac{8}{12}} z^{2}) (4 z^{4})$

Step 1.3

Combine the numerators over the common denominator.

$8 x^{\frac{3 + 1}{7}} y^{\frac{3}{12}} (2 y^{\frac{8}{12}} z^{2}) (4 z^{4})$

Step 1.4

Add $3$ and $1$ .

$8 x^{\frac{4}{7}} y^{\frac{3}{12}} (2 y^{\frac{8}{12}} z^{2}) (4 z^{4})$

Step 2

Multiply $y^{\frac{3}{12}}$ by $y^{\frac{8}{12}}$ by adding the exponents.

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Step 2.1

Move $y^{\frac{8}{12}}$ .

$8 x^{\frac{4}{7}} (y^{\frac{8}{12}} y^{\frac{3}{12}}) (2 z^{2}) (4 z^{4})$

Step 2.2

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

$8 x^{\frac{4}{7}} y^{\frac{8}{12} + \frac{3}{12}} (2 z^{2}) (4 z^{4})$

Step 2.3

Combine the numerators over the common denominator.

$8 x^{\frac{4}{7}} y^{\frac{8 + 3}{12}} (2 z^{2}) (4 z^{4})$

Step 2.4

Add $8$ and $3$ .

$8 x^{\frac{4}{7}} y^{\frac{11}{12}} (2 z^{2}) (4 z^{4})$

Step 3

Multiply $z^{2}$ by $z^{4}$ by adding the exponents.

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Step 3.1

Move $z^{4}$ .

$8 x^{\frac{4}{7}} y^{\frac{11}{12}} (2 (z^{4} z^{2})) \cdot 4$

Step 3.2

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

$8 x^{\frac{4}{7}} y^{\frac{11}{12}} (2 z^{4 + 2}) \cdot 4$

Step 3.3

Add $4$ and $2$ .

$8 x^{\frac{4}{7}} y^{\frac{11}{12}} (2 z^{6}) \cdot 4$

Step 4

Multiply $2$ by $8$ .

$16 x^{\frac{4}{7}} y^{\frac{11}{12}} z^{6} \cdot 4$

Step 5

Multiply $4$ by $16$ .

$64 x^{\frac{4}{7}} y^{\frac{11}{12}} z^{6}$

Step 6

Reorder factors in $64 x^{\frac{4}{7}} y^{\frac{11}{12}} z^{6}$ .

$64 z^{6} x^{\frac{4}{7}} y^{\frac{11}{12}}$