Exponent Rules, Exponents and Exponent Rules, Exponent Rules, Simplifying Exponents, Exponents

4x⁶

(-2x³)²

8x⁶

-4x³(-2x³)

27x⁹

(3x³)³

x⁵

(x²)(x³)

x²

x(x)

-12x²

3x(-4x)

x⁸

x(x⁷)

x⁷

(x⁴)(x³)

12x⁶

(3x)(4x⁵)

8x⁵

(-2x³)(-4x²)

2000x⁶

2x³(10x)³

1/x⁴

x⁻⁴

x⁴y⁴

x²⁴

8x³

9

a⁵

a⁸b¹²

15x⁸

x¹³

x¹⁰

9x²

a⁴

a²¹b⁶

12x⁵

x¹¹

x⁵y⁵

x²⁰

36x²

a⁸

a¹⁸b⁶

4-²

1/16

4x⁶

(-2x³)²

8x⁶

-4x³(-2x³)

27x⁹

(3x³)³

x⁵

(x²)(x³)

x²

x(x)

x³

-x(-x)(x)

6x⁴

-2x(x²)(-3x)

-12x²

3x(-4x)

x⁸

x(x⁷)

-18x⁴

3x²(x²)(-6)

x⁷

(x⁴)(x³)

12x⁶

(3x)(4x⁵)

8x⁵

(-2x³)(-4x²)

-27x⁶

(-3x²)³

2000x⁶

2x³(10x)³

1/x⁴

x⁻⁴

3/x³

3x⁻³

8x³y³

(2xy)³

x¹⁰

x⁴y⁴

x²⁴

8x³

9

a⁵

a⁸b¹²

x⁶/y¹⁰

2c⁷

15x⁸

x¹³

x⁷y⁷

x¹⁰

9x²

a⁴

a²¹b⁶

x⁴/y¹⁰

4c⁵

12x⁵

x¹¹

x⁵y⁵

x²⁰

36x²

a⁸

a¹⁸b⁶

exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself.

base

The number that is multiplied by itself

product rule

When multiplying two powers that have the same base, you can add the exponents.

quotient rule

When dividing two powers that have the same base, you can subtract the exponents.

power to a power rule

When you have an exponent raised to another exponent you keep the base and multiply the exponents.

zero power property

Any nonzero number raised to the power of zero equals 1.

Negative Exponents

To make a negative exponent positive do one of the following:
If the negative exponent is in the numerator position, shift the power to the denominator position.
OR
If the negative exponent is in the denominator position, shift the power to the numerator position.

x² ⋅ x³

x⁵

(x²)⁵

x¹⁰

x² ⋅ x⁵

x⁷

x² ⋅ x⁶

x⁸

(x⁴)³

x¹²

(3x)⁴

81x⁴

(2xy)⁵

32x⁵y⁵

(4x⁵y)³

64x¹⁵y³

(-2x²y⁻⁵)³

-8x⁶y⁻¹⁵

(-5x⁴yz⁸)²

25x⁸y²z¹⁶

2⁻²

¼

4⁰

1

2⁻³

1/8

10⁰

1

5⁻¹

1/5

5⁻³

1/125

15⁻²

1/225

10⁻²

1/100