Problem 54 - Algebra 1

Question

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 13^{5} $$

Step-by-Step Solution

Answer

The fifth power of 13 (\(13^5\)) is 371293.

Step 1: Input the Base

Enter the base (which is 13) into the calculator.

Step 2: Input the Exponent

Now, look for the '^' symbol on the calculator, which represents power or exponent. After finding this button, press the '5' key to input the exponent.

Step 3: Compute

After inputting the base (13) and the exponent (5) in the correct order, press the equal (=) button to find the answer.

Key Concepts

Calculating Powers

When we refer to 'calculating powers,' we're delving into the realm of exponentiation, a fundamental concept in mathematics. It involves raising a number, known as the base, to a certain power, which is the exponent. In simple terms, if you have an expression like \( a^n \), 'a' is the base and 'n' is the exponent, which tells you how many times to multiply the base by itself. The power of a number is the result of this multiplication.

For example, take \( 13^5 \), which means you multiply 13 by itself 4 more times (13 × 13 × 13 × 13 × 13). Calculating this by hand can be time-consuming, hence calculators often come to the rescue. When multiplying a large base or a high exponent, manual calculation becomes impractical, where errors may easily creep in. Therefore, understanding how to correctly raise numbers to a power with the aid of technology is a valuable skill.

Using Calculators for Math

With advancement in technology, using calculators for math has become indispensable. Calculators easily and accurately compute operations which might be challenging manually, like exponentiation. To effectively use a calculator for raising a number to a power, it's crucial to familiarize yourself with the specific symbols and sequence of keys.

Keystroke Tips:

• Identify the buttons: Locate the '^' or 'EXP' button, which is used to indicate an exponent.
• Enter the base first: Type in the number that you're raising to a power.
• Press the exponentiation button: After the base, hit the '^' key.
• Type in the exponent: Enter the number that represents how many times the base is multiplied by itself.
• Compute: Press the equal (=) sign to get the result.

In our example, you would enter '13', press the '^' or 'EXP' button, enter '5', and then '=' to find that \( 13^5 = 371,293 \).

Exponential Expressions

Exponential expressions are mathematical notations that involve exponentiation. The syntax typically involves having a base and an exponent, written in the form of \( a^n \), where \( a \) is the base and \( n \) the exponent. The exponent dictates the number of times the base is multiplied by itself.

Exponential expressions are used extensively across various fields including science, engineering, and finance, to describe growth or decay processes, compound interest, and much more. It's important to differentiate between the base and exponent as they bring vastly different perspectives to a calculation; altering them can lead to significantly different outcomes. Understanding how to manipulate these expressions is crucial, as it's a building block for more complex operations such as logarithms and exponential functions.