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Chapter 7: Problem 14

Evaluate each exponential. $$ 121^{1 / 2} $$

Short Answer

Expert verified
The result of \ 121^{1 / 2} \ is 11.

Step by step solution

01

- Understand the Expression

Identify the base and the exponent in the expression. Here, the base is 121 and the exponent is \(\frac{1}{2}\).
02

- Recall the Meaning of the Exponent

Remember that raising a number to the power of \(\frac{1}{2}\) is the same as finding the square root of the number.
03

- Evaluate the Square Root

Find the square root of 121. The square root of 121 is 11 because 11 multiplied by 11 equals 121.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Base and Exponent Identification
When working with exponentials, identifying the base and exponent is crucial. The **base** is the number that is being multiplied by itself, while the **exponent** indicates how many times the base is used as a factor. In the expression \(121^{1 / 2}\), 121 is the base, and \(\frac{1}{2}\) is the exponent. Recognizing these elements helps in understanding what operation to perform.
Meaning of Exponents
Exponentiation involves raising a base to a power. The exponent tells you how many times to multiply the base by itself. For example:
  • \(2^3 = 2 \times 2 \times 2 = 8\)
  • \(5^2 = 5 \times 5 = 25\)
In our example, the exponent is \(\frac{1}{2}\). This is a special case because an exponent of \(\frac{1}{2}\) means taking the square root. Thus, \(121^{1 / 2}\) is the same as \(\sqrt{121}\), which simplifies the process.
Square Roots
The square root of a number is a value that, when multiplied by itself, gives the original number. For instance:
  • The square root of 9 is 3 since \(3 \times 3 = 9\).
  • The square root of 16 is 4 since \(4 \times 4 = 16\).
In the example \(121^{1 / 2}\), finding the square root of 121 leads to 11, because \(11 \times 11 = 121\). Recognizing this relationship is key for simplifying and solving exponential expressions effectively.

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