# Exponent properties Calculator

## Get detailed solutions to your math problems with our Exponent properties step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### 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

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

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