What exponent would you use to write the power of 10 shown below?
[tex]$10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10=10^? $[/tex]
A. 6
B. 8
C. 0
D. 10
E. 7
F. 9
Answer (2)
Count the number of times 10 is multiplied by itself: 10 × 10 × 10 × 10 × 10 × 10 × 10 .
Recognize that 10 is multiplied by itself 7 times.
Express the product as a power of 10: 1 0 7 .
Conclude that the exponent is 7 .
Explanation
Problem Analysis We are asked to find the exponent to which 10 must be raised to equal the product of the given number of 10s. In other words, we need to determine the value of '?' in the equation 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1 0 ? .
Counting the Multiplications To find the exponent, we need to count how many times 10 is multiplied by itself. In the expression 10 × 10 × 10 × 10 × 10 × 10 × 10 , the number 10 appears 7 times.
Determining the Exponent Therefore, 10 × 10 × 10 × 10 × 10 × 10 × 10 can be written as 1 0 7 . This means the exponent we are looking for is 7.
Final Answer Thus, the exponent that would be used to write the power of 10 is 7 .
Examples
Exponents are a fundamental concept in mathematics and have numerous real-world applications. For instance, consider calculating compound interest. If you invest a principal amount P at an annual interest rate r compounded n times per year for t years, the future value A of the investment is given by the formula A = P ( 1 + n r ) n t . Here, the exponent n t represents the total number of compounding periods. Understanding exponents allows you to accurately predict the growth of your investments over time. For example, if you invest 1000 a t a 5 A = 1000(1 + 0.05)^{10} \approx $1628.89.
The exponent representing the multiplication of 10 seven times is 7 , which can be expressed as 1 0 7 . Therefore, the chosen answer is 7 .
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