Question

Rewrite \(7^3\) as repeated multiplication. A. \(3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\) B. \(7 \cdot 7 \cdot 7\) C. 2187 D. 343

Short answer

Option B: \(7 \cdot 7 \cdot 7\)

Step-by-step solution

Understand the Expression

The expression given is in exponential form: \(7^3\). This means 7 is multiplied by itself 3 times.

Rewrite as Repeated Multiplication

To express \(7^3\) in terms of repeated multiplication, rewrite it as: \(7 \cdot 7 \cdot 7\).

Match with the Given Options

Compare \(7 \cdot 7 \cdot 7\) to the options provided.A. \(3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\)B. \(7 \cdot 7 \cdot 7\)C. 2187D. 343Option B matches \(7 \cdot 7 \cdot 7\).

Key concepts

repeated multiplication

When we talk about exponents like in the expression \(7^3\), we are dealing with repeated multiplication. This means we are multiplying the base number (7) by itself a certain number of times (3 times in this case).

So, \(7^3\) can be broken down as:

• 7 multiplied by 7 equals 49
• then, multiply that result (49) by 7 again

This continuous multiplying is why we call it 'repeated multiplication'. So for \(7^3\), you multiply 7 three times:

\(7 \times 7 \times 7\), which equals 343.

Recognizing repeated multiplication helps us understand how exponents simplify longer calculations.

exponential form

The exponential form is a way to express repeated multiplication in a compact, efficient manner. Instead of writing a long string of the same number multiplied together, we use an exponent.

In the exercise, \(7^3\) is the exponential form. Here, 7 is the base, and 3 is the exponent.

• The base is the number you multiply
• The exponent tells you how many times to multiply the base by itself

Writing numbers in exponential form saves space and simplifies calculations. Instead of \(7 \times 7 \times 7\), we write \(7^3\). This notation is especially useful for working with very large or very small numbers.

mathematical notation

Mathematical notation provides a universal language for expressing mathematical concepts clearly and concisely. Exponents are an essential part of this notation.

When you see \(7^3\), it is a shorthand way of showing multiplication that would otherwise take up more space and time to write out fully.

In addition to representing repeated multiplication, exponents can help:

• Express large numbers
• Simplify scientific calculations
• Quickly convey the scale of something (like population growth)

Understanding how to read and interpret mathematical notation like exponents is key to mastering many areas of math.