Understanding Exponents - Algebra 2

To expand the exponent, we multiply the base by whatever the exponent is.

Although we have two variables, we do know that a number raised to a zero power is one. Therefore:

While a positive exponent says how many times to multiply by a number, a negative exponent says how many times to divide by the number.

To solve for negative exponents, just calculate the reciprocal.

To evaluate a negative exponent, convert the exponent to positive by taking the inverse.

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

Remember that fraction exponents are the same as radicals.

A shortcut would be to express the terms as exponents and look for opportunities to cancel.

Either method, we then need to multiply to two terms.

This problem relies on the key knowledge that and that the multiplying terms with exponents requires adding the exponents. Therefore, we can rewrite the expression thusly:

Therefore, is our final answer.

or

Keep in mind that when you are dividing exponents with the same base, you will want to subtract the exponent found in the denominator from the exponent found in the numerator.

To find the exponent for , subtract the denominator's exponent from the numerator's exponent.

To find the exponent for , subtract the denominator's exponent from the numerator's exponent.

Since the exponent is negative, you will want to put the in the denominator in order to make it positive.

So then,

When you have a number or value with a fractional exponent,

or

So then,

When you have a number or value with a fractional exponent,

or

So then,

When exponents are raised to another exponent, you will need to multiply the exponents together.

When you have a number or value with a fractional exponent,

or

So,

Start by simplifying the numerator. Since two terms with the same base are being multiplied, add the exponents.

Now, when terms with the same bases are divided, subtract the exponent from the denominator from the exponent in the numerator.

The exponent for is

The exponent for is

So then,

An option to solve this is to split up the fraction. Rewrite the fractional exponent as follows:

A value to its half power is the square root of that value.

Substitute this value back into .

Which of the following is equivalent to ?

When dealing with fractional exponents, keep the following in mind: The numerator is making the base bigger, so treat it like a regular exponent. The denominator is making the base smaller, so it must be the root you are taking.

This means that is equal to the fifth root of b to the fourth. Perhaps a bit confusing, but it means that we will keep , but put the whole thing under.

So if we put it together we get:

When dealing with fractional exponents, remember this form:

is the index of the radical which is also the denominator of the fraction, represents the base of the exponent, and is the power the base is raised to. That value is the numerator of the fraction.

When dealing with fractional exponents, remember this form:

is the index of the radical which is also the denominator of the fraction, represents the base of the exponent, and is the power the base is raised to. That value is the numerator of the fraction.

When dealing with fractional exponents, remember this form:

is the index of the radical which is also the denominator of the fraction, represents the base of the exponent, and is the power the base is raised to. That value is the numerator of the fraction.

When dealing with fractional exponents, remember this form:

is the index of the radical which is also the denominator of the fraction, represents the base of the exponent, and is the power the base is raised to. That value is the numerator of the fraction.