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Chapter 5: Problem 89

Explain the quotient rule for exponents. Use \(\frac{3^{6}}{3^{2}}\) in your explanation.

Short Answer

Expert verified
The simplified version of the expression \(\frac{3^{6}}{3^{2}}\) using the quotient rule of exponents is 81.

Step by step solution

01

Understanding the Quotient rule of Exponents

The quotient rule says that when we have an exponential expression with the same base being divided, we can subtract the exponents. The rule is: \(\frac{a^{m}}{a^{n}} = a^{m-n}\) where 'a' is the base and 'm' and 'n' are the exponents.
02

Apply the Rule

To simplify the given expression \(\frac{3^{6}}{3^{2}}\), apply the quotient rule. The base here is '3', while '6' and '2' are the exponents. Subtract 2 from 6 as per the rule: \(3^{6-2}\)
03

Complete the Calculation

After applying the quotient rule, the expression becomes \(3^{4}\) which evaluates to 81 when calculated.

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Most popular questions from this chapter

Use a vertical format to find each product. $$\begin{array}{l}x^{2}+7 x-3 \\\x^{2}-x-1 \\\\\hline\end{array}$$

Perform the indicated computations. Express answers in scientific notation. $$\left(5 \times 10^{3}\right)\left(1.2 \times 10^{-4}\right) \div\left(2.4 \times 10^{2}\right)$$

Use a vertical format to find each product. $$\begin{array}{r}n^{4}-n^{3}+n^{2}-n+1 \\\2 n+3 \\\\\hline\end{array}$$

How do you know if a number is written in scientific notation?

Exercises \(110-112\) will help you prepare for the material covered in the next section. In each exercise, perform the long division without using a calculator, and then state the quotient and the remainder. $$. 9 8 \longdiv { 2 5 . 1 8 7 }$$
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