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Chapter 0: Problem 125

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

Short Answer

Expert verified
Using the power rule, \(\left(3^{2}\right)^{4}\) simplifies to \(3^{8}\).

Step by step solution

01

Understand the Power Rule

The power rule states that \((a^{m})^{n}=a^{m*n}\), where \(a\) is the base, \(m\) is the exponent of the base, and \(n\) is the outer exponent.
02

Apply the Power Rule to Our Example

Using the power rule for the expression \(\left(3^{2}\right)^{4}\), 3 is the base (\(a = 3\)), 2 is the exponent of the base (\(m = 2\)), and 4 is the outer exponent (\(n = 4\)). According to the power rule, the equation simplifies to \(3^{2*4}\).
03

Simplify the Expression

Now, simplify the expression by calculating \(2*4\) in the exponent to get \(3^{8}\).

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Most popular questions from this chapter

$$\text { Factor completely.}$$ $$2 x^{2}-7 x y^{2}+3 y^{4}$$

Determine whether each statement in Exercises 43鈥�50 is true or false. $$-\pi \geq-\pi$$

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}+3 x, \text { for } x=8$$

$$\text { factor completely.}$$ $$(x-5)^{-\frac{1}{2}}(x+5)^{-\frac{1}{2}}-(x+5)^{\frac{1}{2}}(x-5)^{-\frac{3}{2}}$$

$$\text { factor completely.}$$ $$-x^{2}-4 x+5$$
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