Select the best answer for the question.
What is [tex]$6^2$[/tex] in expanded form?
A. [tex]$2 \times 2 \times 2 \times 2 \times 2 \times 2$[/tex]
B. [tex]$6 \times 6$[/tex]
C. 36
D. 12
Answer (1)
The problem asks for the expanded form of 6 2 .
6 2 is equivalent to 6 × 6 .
Compare 6 × 6 with the given options.
The correct answer is B: 6 × 6 .
Explanation
Understanding the Problem We need to find the expanded form of 6 2 . This means we need to express it as a product of its base.
Calculating the Expanded Form 6 2 means 6 multiplied by itself, which is 6 × 6 .
Comparing with Options Now, let's compare this with the given options:
A. 2 × 2 × 2 × 2 × 2 × 2 is 2 6 , which is not equal to 6 2 .
B. 6 × 6 is the correct expanded form of 6 2 .
C. 36 is the result of the calculation 6 × 6 , but it's not the expanded form.
D. 12 is incorrect.
Final Answer Therefore, the best answer is B, which represents 6 2 in its expanded form.
Examples
Understanding exponents is crucial in many real-life scenarios. For example, calculating compound interest involves exponential growth. If you invest $100 at an annual interest rate of 5%, the amount you have after 2 years can be calculated as 100 × ( 1 + 0.05 ) 2 . Here, ( 1.05 ) 2 represents the growth factor, and understanding exponents helps you determine the final value of your investment.
