Thnk you Math Guru The teacher was very impressed with my actually your answer. She asked my how I knew that and I told her about your forum. Thanks Math Guru, Math Buddy. Apr 26 0 Torino - Italy. Math Buddy said:. Jun 10 0 Orlando. I think that the difference between an exponent and a root is that an exponent is a value used as a power to which another value is raised and a root is a number that, when multiplied by itself an appropriate number of times, returns the value under the radical.
Last edited: Jun 23, Similar Math Discussions Math Forum Date What is the difference between a partially ordered set and a totally ordered set? Algebra Nov 4, The sum of the digits of a two-digit number is 18 and the difference between the digits is 3. What is the two- digit number? Notice that the exponent, 3, is the difference between the two exponents in the original expression, 5 and 2. When dividing terms that also contain coefficients, divide the coefficients and then divide variable powers with the same base by subtracting the exponents.
Since the bases of the exponents are the same, you can apply the Quotient Rule. Divide the coefficients and subtract the exponents of matching variables. In the following video we show another example of how to use the quotient rule to divide exponential expressions.
Another word for exponent is power. In this section we will further expand our capabilities with exponents. We will learn what to do when a term with a power is raised to another power, and what to do when two numbers or variables are multiplied and both are raised to an exponent. We will also learn what to do when numbers or variables that are divided are raised to a power. We will begin by raising powers to powers. It is the fourth power of 5 to the second power.
This leads to another rule for exponents—the Power Rule for Exponents. To simplify a power of a power, you multiply the exponents, keeping the base the same. Take a moment to contrast how this is different from the product rule for exponents found on the previous page. Notice that the exponent is applied to each factor of 2 a. So, we can eliminate the middle steps. The product of two or more numbers raised to a power is equal to the product of each number raised to the same power.
How is this rule different from the power raised to a power rule? How is it different from the product rule for exponents on the previous page? Remember that quotient means divide. You can see that raising the quotient to the power of 3 can also be written as the numerator 3 to the power of 3, and the denominator 4 to the power of 3.
Similarly, if you are using variables, the quotient raised to a power is equal to the numerator raised to the power over the denominator raised to power.
When a quotient is raised to a power, you can apply the power to the numerator and denominator individually, as shown below. Simplify by taking 2 to the third power and applying the Power and Quotient Rules for exponents—multiply and subtract the exponents of matching variables. In the following video you will be shown examples of simplifying quotients that are raised to a power. In this section, we will explore what happens when we apply the quotient rule for exponents and get a negative or zero exponent.
To see how this is defined, let us begin with an example. We will use the idea that dividing any number by itself gives a result of 1. This is true for any nonzero real number, or any variable representing a real number. This appears later in more advanced courses, but for now, we will consider the value to be undefined, or DNE Does Not Exist. As done previously, to evaluate expressions containing exponents of 0 or 1, substitute the value of the variable into the expression and simplify.
In the following video there is an example of evaluating an expression with an exponent of zero, as well as simplifying when you get a result of a zero exponent. We proposed another question at the beginning of this section. We will need to use the negative rule of exponents to simplify the expression so that it is easier to understand. Expand the numerator and denominator, all the terms in the numerator will cancel to 1, leaving two h s multiplied in the denominator, and a numerator of 1.
We could have also applied the quotient rule from the last section, to obtain the following result:. This is true when h , or any variable, is a real number and is not zero. Show Solution. Use the quotient rule to subtract the exponents of terms with like bases. Write the expression with positive exponents by putting the term with the negative exponent in the denominator. Write each term with a positive exponent, the numerator will go to the denominator and the denominator will go to the numerator.
Once the rules of exponents are understood, you can begin simplifying more complicated expressions. There are many applications and formulas that make use of exponents, and sometimes expressions can get pretty cluttered.
Simplifying an expression before evaluating can often make the computation easier, as you will see in the following example which makes use of the quotient rule to simplify before substituting 4 for x. Notice that you could have worked this problem by substituting 4 for x and 2 for y in the original expression.
You would still get the answer of 96, but the computation would be much more complex. More classes on this subject Pre-Algebra Discover fractions and factors: Monomials and adding or subtracting polynomials Pre-Algebra Discover fractions and factors: Factorization and prime numbers Pre-Algebra Discover fractions and factors: Finding the greatest common factor Pre-Algebra Discover fractions and factors: Finding the least common multiple.
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