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Exponent properties Calculator

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Example

Solved Problems

Difficult Problems

1

Solved example of exponent properties

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

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

Calculate the power $\sqrt{2}$

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

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

Calculate the power $\sqrt{2}$

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

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

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

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

Calculate the power $\sqrt{2}$

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

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

Calculate the power $\sqrt{2}$

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

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$x^{6}\sqrt{y^{21}z^8}$

$x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$x^{6}z^{4}\sqrt{y^{21}}$

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

Applying the power of a power property

$\frac{\sqrt{2}x^{6}\sqrt{y^{21}z^8}}{40\sqrt{xyz}}$
3

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

$\frac{\sqrt{2}x^{6}\sqrt{y^{21}z^8}}{40\sqrt{xyz}}$

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

Calculate the power $\sqrt{2}$

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

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

Calculate the power $\sqrt{2}$

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

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$x^{6}\sqrt{y^{21}z^8}$

$x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$x^{6}z^{4}\sqrt{y^{21}}$

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

Applying the power of a power property

$\frac{\sqrt{2}x^{6}\sqrt{y^{21}z^8}}{40\sqrt{xyz}}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$z^{4}\sqrt{y^{21}}$

$\frac{\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}}{40\sqrt{xyz}}$

Applying the power of a power property

$\frac{\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}}{40\sqrt{xyz}}$
4

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

$\frac{\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}}{40\sqrt{xyz}}$

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

Calculate the power $\sqrt{2}$

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

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

Calculate the power $\sqrt{2}$

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

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$x^{6}\sqrt{y^{21}z^8}$

$x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$x^{6}z^{4}\sqrt{y^{21}}$

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

Applying the power of a power property

$\frac{\sqrt{2}x^{6}\sqrt{y^{21}z^8}}{40\sqrt{xyz}}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$z^{4}\sqrt{y^{21}}$

$\frac{\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}}{40\sqrt{xyz}}$

Applying the power of a power property

$\frac{\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}}{40\sqrt{xyz}}$
5

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

$\frac{\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}}{40\sqrt{x}\sqrt{yz}}$

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

Calculate the power $\sqrt{2}$

$\sqrt{2}\sqrt{x^{12}y^{21}z^8}$

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

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

Calculate the power $\sqrt{2}$

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

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}\sqrt{y^{21}z^8}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{x^{12}}\sqrt{y^{21}z^8}$

Applying the power of a power property

$x^{6}\sqrt{y^{21}z^8}$

$x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$x^{6}z^{4}\sqrt{y^{21}}$

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

Applying the power of a power property

$\frac{\sqrt{2}x^{6}\sqrt{y^{21}z^8}}{40\sqrt{xyz}}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}$

$\sqrt{y^{21}}\sqrt{z^8}$

Applying the power of a power property

$z^{4}\sqrt{y^{21}}$

$\frac{\sqrt{2}x^{6}\sqrt{y^{21}}\sqrt{z^8}}{40\sqrt{xyz}}$

Applying the power of a power property

$\frac{\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}}{40\sqrt{xyz}}$
6

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

$\frac{\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}}{40\sqrt{x}\sqrt{y}\sqrt{z}}$

Final Answer

$\frac{\sqrt{2}x^{6}z^{4}\sqrt{y^{21}}}{40\sqrt{x}\sqrt{y}\sqrt{z}}$

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