Question

Evaluate the expression. $$3^{2} \cdot 4+8$$

Short answer

The result of the expression \(3^{2} \cdot 4 + 8\) is 44.

Step-by-step solution

Handle Exponents

Compute the part of the expression where exponentiation is used. Here, \(3^{2}\) is equal to 9.

Process Multiplication

The next step is to perform the multiplication. Multiply the result from step 1 with 4. So, \(9 \cdot 4 = 36\)

Finish with Addition

Having handled the multiplication, the last PEMDAS/BODMAS operation is addition. Now, add the result you got in step 2 with 8. Hence, \(36 + 8 = 44\).

Key concepts

Exponentiation

Exponentiation is a mathematical operation involving two numbers, the base and the exponent. In the expression
\(3^{2}\), 3 is the base and 2 is the exponent, and it tells us to multiply 3 by itself 2 times. Thus, \(3^{2} = 3 \times 3 = 9\).
This operation is an essential component of arithmetic and appears in various forms throughout different levels of math. It is crucial to perform exponentiation correctly before moving on to other operations when evaluating expressions.

PEMDAS

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It is a mnemonic aiding in remembering the order of operations to correctly solve math problems.
When you come across an expression like \(3^{2} \times 4 + 8\), PEMDAS guides you to start with any calculations inside parentheses, then move to exponents, followed by multiplication and division from left to right, and finally addition and subtraction in sequence.
It's important to follow this specific order to ensure the accuracy of your solution.

Multiplication

Multiplication is one of the fundamental arithmetic operations. Simply put, it is repeated addition. For instance, \(9 \times 4\) means adding the number 9 to itself 4 times, resulting in 36.
In algebra, when evaluating expressions, multiplication comes after any parentheses or exponents have been addressed. It's also worth noting that multiplication is commutative, meaning that the order of the numbers does not change the result \(9 \times 4 = 4 \times 9\).

Arithmetic Operations

Arithmetic operations are the building blocks of mathematics. They include addition, subtraction, multiplication, division, and exponentiation.
They follow a hierarchical order when combined in expressions. This order is remembered using the PEMDAS rule. Understanding each operation and the order in which to apply them is critical for solving problems accurately.
Each arithmetic operation has unique properties that can simplify calculations, such as the commutative property for addition and multiplication, which allows you to swap the order of the numbers.