Exponents Flashcards
(20 cards)
An exponent is simply,
How many bases to multiply together
Interactions with negative bases between an even or an odd power…
Even: will produce a positive number
Odd: will produce a negative number
Any number to the power of 0…
Will equal 1
Any number to the power of 1
Will be itself
There are only two operations allowed when dealing with exponential terms who share a similar base…
Division (subtract powers) and multiplication (add powers)
Raising a base by a negative power…
Creates a reciprocal. X to negative 2 = 1 X squared.
Two exponent application: (x squared) to the fourth…
X to the eighth
To get similar bases I would…
Use factoring to break down each number and put them in like terms to make the math manageable
Just as you can factor out an exponential terms you can…
Regroup them under one exponent to consolidate the expression
To add and subtract terms with same base…
Pull out common factor to simplify.
13^5 + 13^3 =13^3 ( 13^2 + 1)
Square root aka a fractional exponent
Undoes a square. GMAT only cares about positive roots when given a number under a radical
If you take the root of a number greater than 1…
It’ll become smaller and closer to 1
If you take the root of a positive number less than 1…
It’ll grow and become closer to 1
If you take the root of any positive…
It’ll become closer to 1
Cube rooting of a positive number…
Push number closer to 1
Cube rooting of a negative number…
Will always give a NEGATIVE number
When given an exponent of X/Y…
You can choose whether to raise by X first or take the Y root of the number first. Do what’s easier
Multiply or dividing roots…
Put them all under the same radical sign and treat the sign as a parenthesis. Do the operation and then apply the exponent
How to simplify roots…
Factor out perfect squares to the outside of the radical. 12 aka 4*3 under a square root would be 2 * square root of 3. Each pair of prime factors under the radical turns into a single copy after emerging to the outside
Adding or subtracting roots…
Use factoring to take out the common terms. Similar to adding or subtracting exponents
