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1

Solved example of algebra

$\frac{\sqrt{2x^{12} y^{21} z^8}}{40\sqrt{xy\cdot z}}$
2

The power of a product is equal to the product of it's factors raised to the same power

$\frac{\sqrt{2}\sqrt{x^{12}y^{21}z^8}}{40\sqrt{xyz}}$
3

Take out the constant $\frac{\sqrt{2}}{40}$ from the fraction

$\frac{7}{198}\frac{\sqrt{x^{12}y^{21}z^8}}{\sqrt{xyz}}$
4

Multiplying the fraction and term

$\frac{\frac{7}{198}\sqrt{x^{12}y^{21}z^8}}{\sqrt{xyz}}$
5

The power of a product is equal to the product of it's factors raised to the same power

$\frac{\frac{7}{198}\sqrt{x^{12}}\sqrt{y^{21}z^8}}{\sqrt{xyz}}$
6

Applying the power of a power property

$\frac{\frac{7}{198}x^{6}\sqrt{y^{21}z^8}}{\sqrt{xyz}}$
7

The power of a product is equal to the product of it's factors raised to the same power

$\frac{\frac{7}{198}x^{6}\sqrt{y^{21}}\sqrt{z^8}}{\sqrt{xyz}}$
8

Applying the power of a power property

$\frac{\frac{7}{198}x^{6}\sqrt{y^{21}}\sqrt{z^8}}{\sqrt{xyz}}$
9

Applying the power of a power property

$\frac{\frac{7}{198}x^{6}z^{4}\sqrt{y^{21}}}{\sqrt{xyz}}$
10

The power of a product is equal to the product of it's factors raised to the same power

$\frac{\frac{7}{198}x^{6}z^{4}\sqrt{y^{21}}}{\sqrt{x}\sqrt{yz}}$
11

Simplify the fraction by $x$

$\frac{\frac{7}{198}a^{\left(m-n\right)}z^{4}\sqrt{y^{21}}}{\sqrt{yz}}$
12

The power of a product is equal to the product of it's factors raised to the same power

$\frac{\frac{7}{198}a^{\left(m-n\right)}z^{4}\sqrt{y^{21}}}{\sqrt{y}\sqrt{z}}$
13

Simplify the fraction by $y$

$\frac{\frac{7}{198}a^{\left(m-n\right)}y^{10}z^{4}}{\sqrt{z}}$
14

Simplify the fraction by $z$

$\frac{7}{198}a^{\left(m-n\right)}y^{10}\sqrt{z^{7}}$

Answer

$\frac{7}{198}a^{\left(m-n\right)}y^{10}\sqrt{z^{7}}$

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