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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 for exponents, the expression \( (3^2)^4 \) simplifies down to \( 3^8 \).

Step by step solution

01

Understanding the Power Rule

The Power Rule for Exponents states that for any numbers a, m and n, the term \( (a^m)^n \) is equal to \( a^{mn} \). The exponents m and n are multiplied together.
02

Applying the Power Rule

Now, using the Power Rule, apply it to the given expression \( (3^2)^4 \). The base number is 3, the first exponent is 2 and the second exponent is 4. So, we multiply the exponents 2 and 4 together. This leads to \( 3^{2*4} \).
03

Simplifying the Expression

After you multiply the exponents, the expression simplifies down to \( 3^8 \).

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Most popular questions from this chapter

Simplify using properties of exponents. $$\left(x^{\frac{2}{3}}\right)^{3}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Suppose a square garden has an area represented by \(9 x^{2}\) square feet. If one side is made 7 feet longer and the other side is made 2 feet shorter, then the trinomial that models the area of the larger garden is \(9 x^{2}+15 x-14\) square feet.

Simplify using properties of exponents. $$\frac{\left(2 y^{\frac{1}{5}}\right)^{4}}{y^{\frac{3}{10}}}$$

Explain how to factor \(3 x^{2}+10 x+8\)

Simplify using properties of exponents. $$\left(x^{\frac{4}{5}}\right)^{5}$$
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