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