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Chapter 0: Problem 15

Evaluate the expressions. $$ 2^{2} 2^{-1} 2^{4} 2^{-4} $$

Short Answer

Expert verified
The given expression, \(2^{2} 2^{-1} 2^{4} 2^{-4}\), simplifies to \(2^{1}\), which evaluates to 2.

Step by step solution

01

Recall rules of exponents

Recall the following rules about the exponents: 1. \(a^{m} * a^{n} = a^{m+n}\): When you multiply variables with the same base, add the exponents. 2. \(a^{-n} = \dfrac{1}{a^n}\): A negative exponent means you should flip the base and change the exponent to positive.
02

Simplify the given expression

Apply the rules mentioned above to simplify the expression: \[ 2^{2} 2^{-1} 2^{4} 2^{-4} \] Since all terms have the same base (2), we can add the exponents: \(2^{(2 + (-1) + 4 + (-4))}\)
03

Perform arithmetic operations on exponents

Add the exponents: \(2^{(1 + 0)}\)
04

Simplify the expression

The expression simplifies to: \(2^{1}\)
05

Evaluate the final expression

The final expression evaluates to: \[ 2 \] So, the given expression simplifies to the number 2.

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Most popular questions from this chapter

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3^{2 x-1}+4^{x}-1\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(x^{4}-10 x^{2}+9=0\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(x^{4}-2 x^{2}+1=0\)

Find all possible real solutions of each equation \(y^{3}+3 y^{2}+3 y+2=0\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(x=2-\frac{1}{x}\)
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