Unit 9 Day 1: Exponent Rules
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.
add
To multiply two exponential expressions that have the same base, keep the base and ___ the exponents
multiply
To raise a power to a power, keep the same base and ___ the exponents.
quotient rule
When dividing two powers that have the same base, you can subtract the exponents.
product rule
When multiplying two powers that have the same base, you can add the exponents.
power to a power rule
When you have an exponent raised to another exponent you keep the base and multiply the exponents.
1
a⁷/a⁷
x²
x(x)
x⁸
x(x⁷)
1/x⁴
x⁻⁴
7
√49
square root
An exponent of 1/2 is the same as a
1
10⁰
1/100
10⁻²
√144
12
¼
2^-2
2000x⁶
2x³(10x)³
1/8
2⁻³
-12x²
3x(-4x)
-18x⁴
3x²(x²)(-6)
3/x³
3x⁻³
1
4⁰
5x²
5x⁴/x²
1/125
5⁻³
1/5
5⁻¹
√36
6
exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself.
fraction
A negative exponent indicates that we're dealing with a ____
zero power property
Any nonzero number raised to the power of zero equals 1.
1
Anything raised to the zero power equals
each factor
If a product in parentheses is raised the a power, the parentheses indicate that ___ must be raised to that power.
top
If an element on the bottom of a fraction has a negative exponent it means it belongs on the ____
bottom
If an element on the top of a fraction has a negative exponent it means it belongs on the
coefficient
In the expression 2x, the 2 is called the ___ of x.
base
The number that is multiplied by itself
subtract
To divide two exponential expressions that have the same base, keep the base and ___ the exponents.
-27x⁶
(-3x²)³
25x⁸y²z¹⁶
(-5x⁴yz⁸)²
-5x⁷y³
(10x⁸y⁵)/(-2xy²)
4a
(24a²b) / (6ab)
8x³y³
(2xy)³
32x⁵y⁵
(2xy)⁵
81x⁴
(3x)⁴
27x⁹
(3x³)³
64x¹⁵y³
(4x⁵y)³
x⁵
(x²)(x³)
x¹²
(x⁴)³
6x⁴
-2x(x²)(-3x)
8x⁶
-4x³(-2x³)
-√25
-5
(-8x^6)/y^15
(-2x²y⁻⁵)³
8x⁵
(-2x³)(-4x²)
4x⁶
(-2x³)²
