# 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!

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### Difficult Problems

1

Solved example of exponent properties

$\frac{\left(\left(3x y^2\right)^4\left(2x^3 y^4\right)^3\right)^2}{\left(4x^2 y^3\right)^5}$
2

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

$\frac{\left(\left(3xy^2\right)^4\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2y^3\right)^5}$
3

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

$\frac{\left(\left(3xy^2\right)^4\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$
4

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

$\frac{\left(\left(3xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$
5

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

$\frac{\left(3^4\left(xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$
6

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

$\frac{\left(3^4\right)^2\left(\left(xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$
7

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

$\frac{\left(3^4\right)^2\left(x^4\left(y^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$
8

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

$\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$
9

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

$\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\left(x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$
10

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

$\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$
11

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

$\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$
12

Calculate the power $4^5$

$\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$
13

Calculate the power $3^4$

$\frac{81^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$
14

Calculate the power $81^2$

$\frac{6561\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$
15

Calculate the power $2^3$

$\frac{6561\left(x^4\right)^2\left(\left(y^2\right)^4\right)^28^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$
16

Calculate the power $8^2$

$\frac{6561\cdot 64\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$
17

Multiply $6561$ times $64$

$\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$
18

Simplify $\left(x^2\right)^5$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $5$

$\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}\left(y^3\right)^5}$
19

Simplify $\left(y^3\right)^5$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $3$ and $n$ equals $5$

$\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$
20

Simplify $\left(x^4\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $2$

$\frac{419904x^{4\cdot 2}\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$
21

Simplify $\left(\left(y^2\right)^4\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $2$

$\frac{419904x^{4\cdot 2}\left(y^2\right)^{4\cdot 2}\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$
22

Simplify $\left(y^2\right)^{4\cdot 2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $4\cdot 2$

$\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$
23

Simplify $\left(x^3\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $3$ and $n$ equals $3$

$\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$
24

Simplify $\left(y^4\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $3$

$\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$
25

Multiply $2$ times $5$

$\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{3\cdot 5}}$
26

Multiply $3$ times $5$

$\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$
27

Multiply $4$ times $2$

$\frac{419904x^{8}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$
28

Multiply $2$ times $4$

$\frac{419904x^{8}y^{8\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$
29

Multiply $8$ times $2$

$\frac{419904x^{8}y^{16}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$
30

Multiply $3$ times $3$

$\frac{419904x^{8}y^{16}\left(x^{9}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$
31

Multiply $4$ times $3$

$\frac{419904x^{8}y^{16}\left(x^{9}y^{12}\right)^2}{1024x^{10}y^{15}}$
32

Simplify the fraction $\frac{419904x^{8}y^{16}\left(x^{9}y^{12}\right)^2}{1024x^{10}y^{15}}$ by $y$

$\frac{419904x^{8}y^{\left(16-15\right)}\left(x^{9}y^{12}\right)^2}{1024x^{10}}$
33

Subtract the values $16$ and $-15$

$\frac{419904x^{8}y^{1}\left(x^{9}y^{12}\right)^2}{1024x^{10}}$
34

Any expression to the power of $1$ is equal to that same expression

$\frac{419904x^{8}y\left(x^{9}y^{12}\right)^2}{1024x^{10}}$
35

Simplify the fraction by $x$

$\frac{419904y\left(x^{9}y^{12}\right)^2}{1024x^{\left(10-8\right)}}$
36

Subtract the values $10$ and $-8$

$\frac{419904y\left(x^{9}y^{12}\right)^2}{1024x^{2}}$
37

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

$\frac{419904y\left(x^{9}\right)^2\left(y^{12}\right)^2}{1024x^{2}}$
38

Simplify $\left(x^{9}\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $9$ and $n$ equals $2$

$\frac{419904yx^{9\cdot 2}\left(y^{12}\right)^2}{1024x^{2}}$
39

Simplify $\left(y^{12}\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $12$ and $n$ equals $2$

$\frac{419904yx^{9\cdot 2}y^{12\cdot 2}}{1024x^{2}}$
40

Multiply $9$ times $2$

$\frac{419904yx^{18}y^{12\cdot 2}}{1024x^{2}}$
41

Multiply $12$ times $2$

$\frac{419904yx^{18}y^{24}}{1024x^{2}}$
42

When multiplying exponents with same base you can add the exponents: $419904yx^{18}y^{24}$

$\frac{419904y^{\left(24+1\right)}x^{18}}{1024x^{2}}$
43

Add the values $24$ and $1$

$\frac{419904y^{25}x^{18}}{1024x^{2}}$
44

Simplify the fraction $\frac{419904y^{25}x^{18}}{1024x^{2}}$ by $x$

$\frac{419904y^{25}x^{\left(18-2\right)}}{1024}$
45

Subtract the values $18$ and $-2$

$\frac{419904y^{25}x^{16}}{1024}$

$\frac{419904y^{25}x^{16}}{1024}$