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Exponent Laws

Q: What are the Exponent Laws?

A: There are 4 basic identities to remember:

Example: Example: Example: . . . → Read More: Exponent Laws

Negative and Zero Exponents

Q: What is a negative exponent?

A: A number raised to a negative exponent produces the reciprocal of that number. Recall that a reciprocal is just 1 divided by the number. It is very useful to memorize these identities:

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Q: How do I evaluate a zero exponent?

A: Any number raised . . . → Read More: Negative and Zero Exponents

Arithmetic Sequence

Q: What is an arithmetic sequence?

A: An arithmetic sequence is a sequence of numbers in which the difference between successive numbers is constant. The nth term of an arithmetic sequence is given by:

where a is the first term and d is the common difference.

Adding Radicals

Q: How do I add radicals like this: ?

A: = =

Note that this is analogous to 2x + 4x = 6x, where the terms act similar to the variable x.

Let’s look at some more examples:

= =

Adding Unlike Radicals

Q: What if I have to add radicals, but the radicals are different? I am trying to add .

A: You can’t add those, or simplify any further without a calculator. You just have to leave it as it is, because the square roots are different (3 and 5).

=

Let’s look at . . . → Read More: Adding Unlike Radicals

Subtracting Radicals

Q: How do I subtract radicals like this: ?

A: Subtracting radicals is very similar to adding radicals.

= =

Equation of a Line

Q: What is the equation of a line?

A: The equation of a line is y=mx+b, where

m = slope

b = y-intercept

Q: What is slope?

A: The slope of a line is a measure of how steep the line is. A larger slope means that the line is steeper, while a smaller . . . → Read More: Equation of a Line

Finding the y-intercept

Q: The equation of a line is y=2x -7. What is the y-intercept?

A: It is easy enough to simply compare the equation to the standard form, y=mx+b, and see that b = -7.

However, the general way to find the y-intercept is to set x=0, and solve for y.

y = 2(0) – . . . → Read More: Finding the y-intercept

Finding the Slope

Q: Can you show me how to find the slope of a line with the equation (y+3)=5(x-2)?

A: First, turn the equation into slope-intercept form, y=mx+b. Do this by isolating for y in the equation.

y + 3 = 5x – 10 y = 5x – 10 – 3 y = 5x – 13

. . . → Read More: Finding the Slope

Finding the slope between two points

Q: What is the slope of a line that contains the two points (0,3) and (4,5) ?

A: Recall that the equation for slope is:

You have two points, (0,3) and (4,5), so you have (x1,y1) and (x2,y2). Put them into the formula:

m = (5-3) / (4-0) m = 2 / 4 . . . → Read More: Finding the slope between two points