Problem 48 - Algebra 1

Question

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 2^{10} $$

Step-by-Step Solution

Answer

The result of evaluating \(2^{10}\) using a calculator is 1024.

Step 1: Understand the power notation

Firstly, understand that the power, in this case, '10', indicates how many times '2' has to be multiplied by itself. So, \(2^{10}\) would mean 2 is multiplied by itself 10 times.

Step 2: Calculate using a calculator

Then, use a calculator to calculate \(2^{10}\). Most calculators have a power function. Input the number '2', then choose the power function and input '10'.

Step 3: Interpret the result

Finally, interpret the result that the calculator gives. This will be the result of the power calculation \(2^{10}\).

Key Concepts

Exponentiation

Exponentiation is a fundamental mathematical operation. It involves two numbers: the base and the exponent (or power). In the expression \(2^{10}\), the base is 2 and the exponent is 10. This means 2 should be multiplied by itself 10 times.
Exponentiation is a shortcut for repeated multiplication. Instead of writing 2 × 2 × 2 all the way ten times, it's quicker and neater to simply write \(2^{10}\). This concept becomes especially handy in calculations involving very large or very small numbers. - It helps in understanding growth patterns, like compound interest or population growth. - Vital for scientific calculations, especially in fields such as physics and engineering. Mastering exponentiation will enhance your mathematical toolbox. It simplifies the process of working with numbers that extend beyond basic addition and multiplication.

Calculator Usage

Calculators are powerful tools that assist in complex calculations like exponentiation. Most modern calculators have a dedicated function for computing powers. This function is typically represented by a button labeled with a symbol such as ^ or \(x^y\). To evaluate \(2^{10}\) using a calculator, you can follow these straightforward steps:- Enter the base number, which is 2.- Press the exponentiation button (it varies depending on the calculator model).- Enter the exponent number, which in this case is 10.- Hit the equals (=) button to obtain the result.Using a calculator not only speeds up tasks but also reduces the margin of error in manual computations. Learning to utilize your calculator efficiently improves precision in handling more intricate mathematical problems, especially those involving large exponents.

Mathematical Notation

Mathematical notation is a system of symbols and signs used to represent numbers and operations. It allows complex ideas to be communicated succinctly and clearly. The expression \(2^{10}\) is an example of such notation. - The base, which is written as a larger numeral, tells you what number is being repeatedly multiplied.- The exponent, written as a smaller numeral, tells you how many instances of the base are used in the multiplication. In written and printed math, these notations help streamline communication and make understanding advanced topics more manageable.
Learning to read and write using mathematical notations is like acquiring a new language. It is essential for following mathematics accurately and efficiently across various applications. From simple arithmetic to advanced calculus, mathematical notation is the universal language of numbers.