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Exponent properties Calculator

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Example

Solved Problems

Difficult Problems

1

Solved example of exponent properties

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

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 $x$

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

12

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

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

Answer

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

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