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Chapter 4: Problem 49

Write a multiplication expression whose product is \(5^{3}\).

Short Answer

Expert verified
The multiplication expression is \(5 \times 5 \times 5\).

Step by step solution

01

Understand the Expression

The expression you're looking for is a multiplication expression that multiplies certain numbers to give the result equivalent to \(5^3\). The number \(5^3\) is known as five raised to the power of three, which equals multiplying 5 by itself three times.
02

Break Down the Power

A power of a number, such as \(5^3\), is just a repeated multiplication. In mathematical terms, \(5^3 = 5 \times 5 \times 5\). This means you need to multiply the number 5 by itself a total of three times.
03

Write the Multiplication Expression

Based on the breakdown, the multiplication expression that gives the product \(5^3\) is \(5 \times 5 \times 5\). This expression directly represents the meaning of the power in the original equation.

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Key Concepts

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

Multiplication Expression
A multiplication expression is a mathematical setup where numbers or variables are multiplied together. These expressions use the multiplication operator, which is often symbolized by the cross sign (\(\times\)). When you want to express the multiplication of numbers, you'll place the numbers side by side with this operator. For example:
  • The multiplication expression \(5 \times 5 \times 5\) illustrates the process of multiplying 5 with itself twice more.
  • Note that multiplication expressions are commutative, meaning \(a \times b = b \times a\).
The multiplication expression forms the foundation of understanding powers and exponents as it visually communicates repeated multiplication.
Powers of Numbers
The concept of powers of numbers, sometimes known as exponents, is a shorthand notation that tells us how many times a number must be multiplied by itself. This is particularly useful for large calculations or expressing repetitive multiplication concisely.
  • The notation \(a^n\) indicates that the number \(a\) is to be multiplied by itself \(n\) times.
  • \(5^3\) means you multiply 5 by itself three times: \(5 \times 5 \times 5\).
  • Powers also make calculations quite handy, for instance, simplifying big multiplications such as \(2^{10}\), which is compactly written and computed easier than multiplying ten 2s together.
Understanding powers helps in recognizing patterns and solving problems efficiently. The base and the exponent are critical to decoding the strength of a power.
Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, and operations that represent values or relationships. They form the language of mathematics, allowing us to communicate mathematical ideas clearly and logically.
  • An expression can be as simple as a single number (e.g., 7) or as complex as a polynomial \((x^2 + 5x + 6)\).
  • Expressions like \(5 \times 5 \times 5\) are specific cases that show multiplication and powers.
  • Mathematical expressions do not contain equality or inequality signs; those would make them equations or inequalities respectively.
Working with expressions allows you to perform arithmetic, solve problems, and represent complex mathematical relationships in simpler ways.

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Most popular questions from this chapter

Write each fraction in simplest form. If the fraction is already in simplest form, write simplified. $$\frac{30}{37}$$

A number is divided by \(-6,\) and the result is \(24 .\) What is the original number?

Find each product or quotient. Express using exponents. $$\frac{y^{9}}{y^{2}}$$

Find each equivalent measure. $$1 \mathrm{m}=\underline{?} \mathrm{cm}$$

Use the Distributive Property to rewrite each expression. $$-5(a-10)$$
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