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Chapter 0: Problem 101

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

Short Answer

Expert verified
Using the power rule for exponents, \(\left(3^{2}\right)^{4} = 3^{8}\)

Step by step solution

01

Understand the power rule for exponents

The power rule for exponents states that for any number 'a', and integers 'm' and 'n', \((a^{m})^{n} = a^{mn}\). This means that when an exponential expression is raised to a power, the powers multiply.
02

Apply the power rule to the given example

Apply the rule to the given example, \(\left(3^{2}\right)^{4} = 3^{(2*4)}\). This follows directly from the power rule.
03

Calculate the value

Now compute the value of the expression: \(3^{(2*4)} = 3^{8}\).

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Most popular questions from this chapter

Find all numbers that must be excluded from the domain of each rational expression. $$ \frac{x+7}{x^{2}-49} $$

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$ \frac{y^{2}+7 y-18}{y^{2}-3 y+2} $$

Use the quotient rule to simplify the expressions in Exercises \(17-26 .\) Assume that \(x>0\) $$\frac{\sqrt{150 x^{4}}}{\sqrt{3 x}}$$

In Exercises \(1-10\), factor out the greatest common factor. $$6 x^{4}-18 x^{3}+12 x^{2}$$

Use the product rule to simplify the expressions in Exercises \(7-16 .\) In Exercises \(11-16,\) assume that variables represent nonnegative real numbers. $$\sqrt{45 x^{2}}$$
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