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Problem 1

# Evaluate the expressions in Exercises 1-16. $$3^{3}$$

Expert verified
The expression $$3^3$$ evaluates to 27 by following exponentiation rules: $$3^3 = 3 \times 3 \times 3 = 9 \times 3 = 27$$.
See the step by step solution

## Step 1: Understand exponentiation

Exponentiation is an operation that raises the base number to the power of an exponent. In general, exponentiation can be represented as $$a^n$$, where $$a$$ is the base number, and $$n$$ is the exponent. The result is obtained by multiplying the base number with itself (n-1) times.

## Step 2: Apply exponentiation to the given expression

In the given expression $$3^3$$, the base number is 3, and the exponent is also 3. According to the exponentiation rule, we need to multiply the base number (3) with itself (3-1 = 2) more times.

## Step 3: Calculate the result

To evaluate the expression $$3^3$$, we will perform the following multiplications: $$3^3 = 3 \times 3 \times 3 \\ 3^3 = 9 \times 3 \\ 3^3 = 27$$ The result of the expression $$3^3$$ is 27.

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