An exponent refers to the number of times the base is a factor. For example, . For a term with a coefficient in front of a variable raised to an exponent, it’s important to remember that the exponent only affects the variable. Knowing the order of operations is helpful to avoid simple exponent mistakes. For , first you would square x and then multiply the result by 2.
Any number to the ^2 power is referred to as being “squared.” Any number to the ^3 power is called being “cubed.”
When you multiply two terms with the same base, you can add the exponents:
When you divide two terms with the same base, you can subtract the exponent of the numerator from the exponent of the denominator:
If two exponents are separated by a parenthesis, you can multiply them:
On the GMAT look for ways to rewrite bases so they are the same.
There is no quick way of combining exponents when the bases are added. Don’t be fooled if you see something like ?. The answer is NOT . To solve, you must multiple out each term and then find the sum.
Any nonzero number raised to a power of zero is equal to 1.
However = undefined.
A negative exponent is another way of expressing a fraction:
A fractional exponent is another way of expressing a root:
When a fraction is raised to an exponent, you must distribute the power both to the numerator and the denominator:
Notice how the fraction will actually decrease in number as the exponent increases.
A negative number raised to an even exponent will always be positive. The negative sign will cancel itself out.
However a negative numbers raised to an odd exponent will remain negative.
Large numbers and very small decimals are often expressed with exponents using scientific notation. Scientific notation involves writing the number as a product of a decimal and the number 10 raised to a certain power.
The number of the exponent indicates the number of places the decimal moves.
zeros = 10,000,000
(the decimal moves four places to the right)
(Since it’s a negative exponent, the decimal will move to the left.)