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Chapter 5: Problem 14

Simplify each expression using the power rule. $$\left[(-50)^{4}\right]^{4}$$

Short Answer

Expert verified
Therefore, the simplified expression for \(\left[(-50)^{4}\right]^{4}\) is \((-50)^{16}\) , which is a positive number.

Step by step solution

01

Understand the power rule

The power rule states that when we raise a power to another power, we need to multiply the exponents. In our case, we have \((-50)^{4}\) raised to the power of 4, i.e., \(\left[(-50)^{4}\right]^{4}\) . Here, -50 is your base, and 4 is the exponent.
02

Apply the power rule

We multiply the exponents (the 4 inside the square bracket and the 4 outside) as they both apply to the same base. So, \(\left[(-50)^{4}\right]^{4}\) becomes \((-50)^{4*4}\)
03

Simplify the expression

Next, multiply 4*4 to get 16. So, the expression \((-50)^{4*4}\) becomes \((-50)^{16}\)
04

Find the value of the expression

At this stage, we know that any number raised to an even power gives a positive result. Hence, \((-50)^{16}\) simplifies to a positive number.

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