# Solving Exponential Problems

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Now, we can "cancel" any instance of a factor that appears in both the numerator and denominator. Recall that we were able to find equivalent fractions by multiplying (or dividing) both the numerator and denominator by a particular value-this is equivalent to multiplying or dividing by one.Later in the course, we will consider fractional exponents.(As it turns out, fractional exponents obey the same rules as integer exponents, but the precise meaning of a fraction will be made clear later on.) Although exponents may at times seem like an obscure or less than practical mathematical tool, they have numerous important and practical applications.Note also the usefulness of these rules of exponents in part d: multiplying 150 twenty (or twenty-six) times is a tough proposition, and even most calculators cannot provide an exact product.The use of exponents, however, allows us to have an Notice that the expanded form has four factors of 2 and four factors of 3.Exponential functions often involve the rate of increase or decrease of something.When it's a rate of increase, you have an exponential growth function!We can see that the exponent of the answer is the difference between that of the numerator and that of the denominator (again, all have the same base).Let's generalize the rule: Notice that the expression in parentheses has three factors, and we must multiply this expression four times.This expression is the same as the following (multiplication is commutative, so we can rearrange the factors in the product).If you consider division of exponential expressions, you may notice that the rule seems to indicate that we can end up with negative exponents.

• ###### Exponential Equations - West Texas A&M University

Mar 24, 2011. Now that the variable is out of the exponent, solve for the variable using inverse operations to complete the problem.…

• ###### The Mathematical Rules of Solving Exponent Problems.

The Mathematical Rules of Solving Exponent Problems. Key Terms. o Scientific notation. Objectives. o Derive the rules for multiplying and dividing exponential.…

• ###### Sample Exponential and Logarithm Problems 1 Exponential.

Sample Exponential and Logarithm Problems. 1 Exponential Problems. Example 1.1 Solve. 1. 6. −3x−2. = 36x+1. Solution Note that. 1. 6. = 6−1 and 36 = 62.…

• ###### Solve Exponential and Logarithm Problems

Problem 1 The population P of a city increases according to the formula. P = 5000 e a t. where t is in years and t = 0 corresponds to 1980. In 1990, the.…

• ###### How Do You Solve a Word Problem with Exponential Growth.

Note If something increases at a constant rate, you may have exponential growth on your hands. In this tutorial, learn how to turn a word problem into an.…

• ###### Solve applied problems involving exponential and logarithmic.

Solve applied problems involving exponential and logarithmic equations. In previous sections, we learned the properties and rules for both exponential and.…

• ###### Exponential Functions – She Loves Math

Also note that Factoring with Exponents and Solving Exponential Equations after. Note that you can also solve half-life problems using the next formula.…

• ###### Lesson 21 Logarithmic and Exponential Problem Solving

This lesson uses the context of radiocarbon dating to understand and apply the inverse relationship between logarithms and exponents when solving problems.…