Problem 30 Evaluate each expression. $$3 ... [FREE SOLUTION]

Chapter 4: Problem 30

Evaluate each expression. $$3 \cdot 4^{2}$$

Short Answer

Expert verified

The value of the expression is 48.

Step by step solution

Calculate the Exponent

First, evaluate the expression inside the exponent. We need to calculate what $ 4^2 $ is. $ 4^2 $ means 4 multiplied by itself: $ 4 \times 4 $. The result is 16.

Multiply by the Coefficient

Now that you know $ 4^2 $ equals 16, multiply this result by the coefficient in front of the exponent, which is 3. Perform the multiplication: $ 3 \times 16 $. This gives us 48.

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Key Concepts

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

Exponents

Exponents are a way to express repeated multiplication of a number by itself. For example, when you see $4^2$, it means 4 is multiplied by itself once (i.e., $4 \times 4$). Exponents are also called powers and have a base and an exponent number. In $4^2$, 4 is the base and 2 is the exponent.
Understanding exponents is crucial in mathematics, especially in pre-algebra and algebra. They help simplify expressions that involve large repeated multiplications and are foundational for exploring more advanced topics. Remember; exponents are calculated before any other operations when evaluating expressions. This is where our next topic, the "Order of Operations," becomes important.

Multiplication

Multiplication is a fundamental arithmetic operation. It involves adding a number (the multiplicand) to itself a specific number of times defined by another number (the multiplier). In the exercise, after calculating the exponent, you perform multiplication: $3 \times 16$.
When multiplying numbers, it is helpful to think about grouping. For instance, saying $3 \times 16$ could mean you have three groups of 16, which you can add to find the same result. But multiplication is quicker and more efficient, especially with larger numbers, as it reduces long addition to a much simpler, single step.

Order of Operations

The order of operations is a set of rules that tells you which steps to perform first in an expression. The common acronym is PEMDAS or BIDMAS (depending on your region), which stands for:

Parentheses/Brackets
Exponents/Indices
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Understanding this order is key for solving equations correctly. In our exercise, the exponent $4^2$ is calculated before the multiplication because exponents come before multiplication in the order of operations. This ensures that everyone solves the expression in the same way and arrives at the same answer.

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91影视

Evaluate each expression. $$3 \cdot 4^{2}$$

Short Answer

Step by step solution

Calculate the Exponent

Multiply by the Coefficient

Key Concepts

Exponents

Multiplication

Order of Operations

One App. One Place for Learning.

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