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Chapter 1: Problem 28

\(7^{2}\)

Short Answer

Expert verified
The value of \(7^2\) is 49.

Step by step solution

01

Understand the Exercise

The exercise asks for the value of the expression \(7^2\). This means we need to multiply the number 7 by itself.
02

Perform the Calculation

Calculate \(7 \times 7\). Multiplying these two numbers gives \(49\).
03

Write the Answer

The value of \(7^2\) is \(49\).

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Key Concepts

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

Squared Number
A squared number is the result of multiplying a number by itself. For example, when you see an expression like \(7^2\), it means you need to multiply 7 by 7.
This operation is essential in many areas of mathematics, such as geometry and algebra.
A few more examples of squared numbers include:
  • \(5^2 = 25\)
  • \(3^2 = 9\)
  • \(10^2 = 100\)

Squaring helps in finding the area of squares when you know the length of one side.
It is also a stepping stone to understanding higher powers of numbers.
Multiplication
Multiplication is one of the basic arithmetic operations. It involves adding a number to itself a certain number of times.
For instance, when you perform \(7 \times 7\), you're effectively adding 7 to itself seven times:
\[7 + 7 + 7 + 7 + 7 + 7 + 7 = 49\]
In the context of exponentiation, multiplication is used to compute powers such as \(7^2\).
Multiplication is a fundamental skill that is necessary for solving a range of mathematical problems.

When multiplying numbers, it's helpful to remember the multiplication facts for quick calculations.
Here are a few examples:
  • \(2 \times 3 = 6\)
  • \(4 \times 5 = 20\)
  • \(6 \times 8 = 48\)
Powers of Numbers
Powers of numbers are expressions where a number is multiplied by itself a certain number of times.
The expression is written as \(a^b\), where \(a\) is the base and \(b\) is the exponent.
This notation signifies how many times the base number is multiplied by itself.
In the case of \(7^2\), the base is 7 and the exponent is 2, so \(7\) is multiplied by itself once.
Here are some more examples to illustrate:
  • \(3^4 = 3 \times 3 \times 3 \times 3 = 81\)
  • \(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\)
  • \(5^3 = 5 \times 5 \times 5 = 125\)

Understanding powers is crucial in algebra and higher-level math topics.
They simplify the expression and handling of large numbers in calculations.

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Most popular questions from this chapter

A furniture store bought a recliner from a wholesaler for \(\$ 150\). It then sold the recliner for \(\$ 499\). Find the percent markup. Round to the nearest percent.

Evaluate \(12 \mathrm{~kg}+54 \mathrm{~g}\). Write the answer in grams.

Problem: Find the simple interest earned on \(\$ 300\) invested for 5 years at an annual simple interest rate of \(4.5 \%\). Incorrect Answer: \(I=P R T\) $$ \begin{aligned} &I=(\$ 300)\left(\frac{4.5}{1 \text { year }}\right)(5 \text { years }) \\ &I=\$ 6750 \end{aligned} $$

Evaluate \(8 \mathrm{~km}+4 \mathrm{~m}\). Write the answer in kilometers.

The shape of a table top is a trapezoid with bases that measure \(25 \mathrm{in}\). and \(60 \mathrm{in}\). The height is \(30 \mathrm{in}\). Find the area of this table.
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