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Chapter 5: Problem 12

Simplify each expression using the power rule. $$\left(x^{12}\right)^{4}$$

Short Answer

Expert verified
The simplified form of \((x^{12})^{4}\) is \(x^{48}\).

Step by step solution

01

Recognize the Form

Recognize that the expression \(x^{12}\) raised to the fourth power can be written in the form \((a^m)^n\). Here, 'a' is 'x', 'm' is '12', and 'n' is '4'.
02

Apply the Power Rule

According to the power rule, the solution equals to \(a^{m \cdot n}\). Replace 'a' with 'x', 'm' with '12', and 'n' with '4'. That means the solution can be written as \(x^{12 \cdot 4}\).
03

Solve the Expression

Multiply the exponents together. The expression \(x^{12 \cdot 4}\) becomes \(x^{48}\).

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