Problem 16 Expand the exponential expressio... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 1: Problem 16

Expand the exponential expression as a repeated multiplication. Do not simplify. $$2^{6}$$

Short Answer

Expert verified

2 $ \times $ 2 $ \times $ 2 $ \times $ 2 $ \times $ 2 $ \times $ 2

Step by step solution

Identify the Base and Exponent

The base of the exponential expression is the number being multiplied, which is 2. The exponent is the number of times the base is multiplied by itself, which is 6.

Write the Base Repeatedly

Write the base, 2, six times in a row: 2, 2, 2, 2, 2, 2.

Insert Multiplication Signs

Place multiplication signs ($ \times $) between each instance of the base: 2 $ \times $ 2 $ \times $ 2 $ \times $ 2 $ \times $ 2 $ \times $ 2.

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Key Concepts

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

headline of the respective core concept

An exponential expression consists of two parts: the base and the exponent. The base is the number that is being multiplied. In our exercise, the base is 2. The exponent tells us how many times to multiply the base by itself. In the exercise, the exponent is 6. This means we are multiplying the base, which is 2, a total of six times.

headline of the respective core concept

Exponential expressions are essentially a more compact way of representing repeated multiplication. Writing an exponential expression like this: $$2^{6}$$ simply means that we are multiplying the base, 2, repeatedly six times. When we expand this, we get: 2 \times 2 \times 2 \times 2 \times 2 \times 2. It's that easy! This method is especially useful when dealing with large numbers or higher exponents.

headline of the respective core concept

Understanding exponential expressions is a key concept in mathematics education, useful in various topics such as algebra, calculus, and scientific notation. It builds foundational skills important for:

Solving equations
Understanding growth and decay
Working with scientific data

When students are comfortable with exponential expressions, it makes learning more advanced concepts much easier. It's important to practice converting exponential forms to repeated multiplication to gain a solid understanding.

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91影视

Expand the exponential expression as a repeated multiplication. Do not simplify. $$2^{6}$$

Short Answer

Step by step solution

Identify the Base and Exponent

Write the Base Repeatedly

Insert Multiplication Signs

Key Concepts

headline of the respective core concept

headline of the respective core concept

headline of the respective core concept

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