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Chapter 0: Problem 16

Evaluate the expressions. $$ 5^{2} 5^{-3} 5^{2} 5^{-2} $$

Short Answer

Expert verified
The simplified expression is \(5^1\), so the final answer is 5.

Step by step solution

01

Identify the base and exponents

First, let's identify the bases and the exponents in the given expression. In this case, our base is 5 and we have various exponents: 2, -3, 2, and -2. The expression is: \(5^2 \cdot 5^{-3} \cdot 5^2 \cdot 5^{-2}\)
02

Apply properties of exponents

Now we'll apply the properties of exponents. When the bases are the same, and we are multiplying the numbers, we can add their exponents. So, our expression becomes: \(5^{(2 + (-3) + 2 + (-2))}\)
03

Simplify the expression

Now, we'll simplify the expression by performing the addition within the parentheses. \(5^{(2 - 3 + 2 - 2)} = 5^{(-1 + 2)} = 5^{1}\)
04

Final answer

Since our simplified expression is \(5^1\), the final answer is 5, as any number raised to the power of 1 is the number itself.

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Most popular questions from this chapter

Giving the answer as \(a\) whole number or a fraction in lowest terms. $$ 3+([4-2] \cdot 9) $$

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3.1 x^{3}-4 x^{-2}-\frac{60}{x^{2}-1}\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(\frac{4 \times 2}{\left(\frac{2}{3}\right)}\)

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. \(x^{4}+x^{2}-1=0\)
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