91Ó°ÊÓ

In math, an exponent tells us how many times to multiply a number by itself. It's a way to simplify repeated multiplication. For example, when we see \(r^n\), it means we need to multiply \(r\) by itself \(n\) times. In our problem, \(r = 3\) and \(n = 2\). So, we calculate \(3^2\), which means \(3 \times 3\). This equals 9.

• Basis: The number that's being multiplied (here, \(r\)).
• Exponent: The number of times the base is multiplied by itself (here, \(n\)).

Here's the general formula for dealing with exponents:i.e. \(b^e = b \times b \times ... \times b\) (\(e\) times).If you understand this one, you'll master the concept of exponents easily. Practice with different numbers to build a stronger understanding!

Basic algebra involves working with variables and constants to form equations and solve them. In our given problem, we have an expression: \(ar^n\). Here:

• \(a\) is a constant.
• \(r\) is a constant which will be raised to a power \(n\).

In algebra, our task often involves substituting values for these variables and performing arithmetic operations to find the final result. It's like following a recipe:

1. Identify your variables and constants (we did this in Step 1).
2. Substitute them into the algebraic expression (we understood the expression in Step 2).
3. Perform the arithmetic operations in the correct order (we calculated the exponent and multiplied by \(a\) in Steps 3 and 4).Understanding algebraic expressions and how to manipulate them is a foundational skill in math.

Multiplication is one of the basic arithmetic operations. It is represented by symbols like x or \times. In multiplication, you take two numbers and add one of them to itself as many times as the other number indicates. For example: \(2 \times 3\) means add 2 three times: \(2 + 2 + 2 = 6\). In our problem, after finding the exponent result \(3^2 = 9\), we used multiplication by \(a (which is 2)\). Here's how it works: First, find the result of the exponentiation which is \( 3^2 = 9\). Next, multiply this result by 2: \(2 \times 9 = 18\). This kind of operation is crucial and comes very often in all of algebra and calculus. Practice different multiplication problems to become confident in this skill!