Helpful Hints to ALWAYS Remember:
-
Can write any number/variable with a negative exponent as a fraction with “1” over that
variable/exponent (definition of a negative exponent)
- Example: 8-1 = 1 or x-3 = 1
8
x3
-
Any fraction with a numerator of “1”, can be written as the (denominator) to the -1 power
Example: 1 = 2-1
1 = 4-1
2
4
-
A number/variable with a negative exponent in the denominator can be moved to numerator to make it
positive, and vice versa, so that 2x3 = 2x3y4 or
3x-2y = 3y
y-4
4
4x2
-
When multiply powers with the same base, you ADD the exponents (product of powers property)
- Example: 24 * 28 = 28+2 = 210 = 1,024
-
When you divide powers with the same base, you SUBTRACT the exponents (quotient of powers property)
- Example: 210 = 210-4 = 26 = 64
24
-
When you find the power of a power, you MULTIPLY the exponents (power of a power property)
- Example (23)2 = 23*2 = 26 = 64. (you distribute the power to each exponent)
-
When you multiply and two numbers/variables inside parenthesis and then raise to a power, apply the
power to each. number in the parenthesis (power of product property)
- Example (3 * 5)3 =. 33 * 53 = 27 * 125 = 3,375
-
When solving exponential equations,
- Try and find same base, look to see what smallest number (called the “factor”) that will divide into
each side of the number/variable of the equation
§ Example: 2x = 16x+2, so smallest number that goes in to 2 and 16, is 2
2 1 2 8
2 4
2 2
So can re-write equation as 2x = 24(x+2)
-
Simplify the exponents if needed, so in example above, on the right side, 4(x+2) simplifies to (4x+2)
Once find same base, can drop the base and set the exponents equal and solve
§ So in example above where end up with 2x = 24(x=2) can then solve by setting
x = 4x+2 and solve for x
-
Any number to power of 0 is ALWAYS 1, so that 20 = 1 or 1250 = 1
-
When graphing make sure one side is equal to zero, so either add or subtract from one side to get zero on
one side of equal sign.