Exponents
Help Questions
GED Math › Exponents
Write the following expression in expanded form:
Explanation
An exponent indicates the amount of times a number (or variable) should be multiplied by itself. For example, .
In this instance, .
Simplify the following expression:
Explanation
Simplify the following expression:
To combine these, we need to multiply the coefficients and add our exponents.
Solve:
Explanation
Order from least to greatest:
Do not use a calculator.
Explanation
For any nonzero and for any
,
.
Also, any negative number raised to the power of an odd number is equal to the opposite of the same power of its absolute value.
Combine these concepts:
Since ,
the reciprocals are in reverse order of this:
Their opposites reverse again:
Or, equivalently,
.
Combine the following:
Explanation
To multiply variables with exponents, we will use the following formula:
Now, let’s combine the following:
What is the product of ?
Explanation
Start by distributing the exponents into their respective terms. Recall that when an exponent is raised to an exponent, you will need to multiply the exponents together.
Next, multiply like terms together. Recall that when you multiply numbers that have the same base, you will need to add the exponents together.
Divide the following:
Explanation
To divide variables with exponents, we will use the following formula:
Now, let’s divide. We get
Evaluate and
. Which statement is true of these two values?
and
and
Explanation
has 6, an even number, as an exponent, so
is a positive number, and it can be calculated by taking sixth power of 3.
is the (negative) opposite of the sixth power of 3.
Therefore,
and
.
Explanation
Remember that for negative exponent values, you "flip" the number over the bar of the fraction of which it is a part. When you do this, you then make its power positive. You should always start by doing this. It makes it easier for most students to understand the reductions that follow upon that.
Thus, for your value, you know:
Combine your like variables first. You do this by adding their exponents:
Luckily, there is no canceling for you to do!
Order from least to greatest:
Do not use a calculator.
Explanation
For any nonzero and for any
,
.
Since ,
we can reverse the order when taking their reciprocals:
That is, .