Simplify (8x^(1/7)y^(3/12))(2y^(8/12)z^2)(4x^(3/7)z^4)

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

Step 1

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

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

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

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

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

Combine the numerators over the common denominator.

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

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.

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

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

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

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

Combine the numerators over the common denominator.

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

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.

Move $z^{4}$ .

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

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

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

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

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