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Chapter 5: Problem 18

Evaluate each expression for a 2 and b 3. $$ 4^{a} $$

Short Answer

Expert verified
16

Step by step solution

01

Understand the Given Values

We are given two values: \(a = 2\) and \(b = 3\). In this exercise, only \(a\) is needed.
02

Identify the Expression to Evaluate

The expression to evaluate is \(4^{a}\).
03

Substitute the Value of \(a\)

Replace \(a\) in the expression with the value 2. Thus, the expression becomes \(4^{2}\).
04

Perform the Calculation

Evaluate \(4^{2}\). The calculation is \(4 \times 4 = 16\).

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Key Concepts

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

substitution in algebra
Substitution is a fundamental concept in algebra. It means replacing variables in an expression with their given numerical values.
In our exercise, we substitute the value of 'a' directly into the expression.
This method simplifies complex algebraic expressions and converts them to simple calculations.
Here's how you can do it:
  • Identify the variable you need to substitute.
  • Replace this variable with its given value.
  • Simplify the resulting expression.
For instance, given the expression, we have identified 'a' as 2. So we substitute 'a' with 2, making the expression easy to solve.
exponentiation
Exponentiation refers to raising a number to the power of another number. The base is the number being multiplied, and the exponent tells us how many times to multiply the base by itself.
In our example, the expression is 4^a<, where 4 is the base and a is the exponent.
After substitution, the expression becomes 4^2.
This means we multiply 4 by itself twice:
  • 4 * 4 = 16
Exponentiation is essential in mathematics as it helps solve problems involving growth, areas, and many other calculations. It makes handling large numbers feasible.
basic arithmetic operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. In our exercise, after substituting the value of 'a', we perform multiplication:
4 * 4.
  • Multiplication combines repeated addition.
  • For instance, 4 * 4 can also be viewed as 4 added to itself 4 times:
4 + 4 + 4 + 4 = 16
Mastering basic arithmetic is vital as it forms the foundation of more complex mathematical concepts.
It allows us to solve real-world problems efficiently. In this exercise, basic multiplication helped us find the value of 4^2.

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