What exponent would you use to write the power of 10 below?
[tex]$10 \times 10=10^? $[/tex]
A. 2
B. 5
C. 5
D. 0
E. 1
F. 3
Answer (2)
Calculate the left side of the equation: 10 × 10 = 100 .
Express 100 as a power of 10: 100 = 1 0 2 .
Identify the exponent: The exponent is 2.
The equation is 10 × 10 = 1 0 2 , so the answer is 2 .
Explanation
Understanding the Problem We are given the equation 10 × 10 = 1 0 ? . Our goal is to find the exponent that makes this equation true.
Calculating the Left Side First, let's calculate the value of 10 × 10 .
Result of Multiplication 10 × 10 = 100
Expressing as a Power of 10 Now, we need to express 100 as a power of 10. In other words, we want to find '?' such that 100 = 1 0 ? .
Identifying the Exponent We know that 1 0 2 = 10 × 10 = 100 . Therefore, the exponent we are looking for is 2.
Final Answer So, 10 × 10 = 1 0 2 .
Examples
Understanding exponents is crucial in many areas, such as calculating compound interest. For example, if you invest $100 and it grows at a rate of 10% per year, after two years, the investment will be $100 \times (1 + 0.10)^2 = $100 \times 1.1^2 = $100 \times 1.21 = $121. This shows how exponents help calculate growth over time.
The exponent used to express 10 × 10 as a power of 10 is 2, since 10 × 10 equals 100, which can be written as 1 0 2 . Therefore, the answer is \boxed{2}.
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