What exponent would you use to write the power of 10 below?
[tex]$10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10=10^? ?$[/tex]
A. 6
B. 11
C. 9
D. 10
E. 8
F. 100
Answer (2)
Count the number of times 10 is multiplied by itself.
Recognize that 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 means 10 is multiplied by itself 9 times.
Express the product as a power of 10: 1 0 9 .
The exponent is 9 .
Explanation
Problem Analysis We are asked to find the exponent that expresses the given product of 10s as a power of 10.
Counting the Factors We need to count how many times 10 is multiplied by itself. In the expression 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 , the number 10 appears 9 times.
Expressing as a Power of 10 Therefore, the expression can be written as 1 0 9 .
Final Answer The exponent is 9.
Examples
Understanding exponents is crucial in many fields, such as computer science and finance. For example, when measuring computer memory, we often use powers of 2 (e.g., kilobytes, megabytes, gigabytes). Similarly, in finance, compound interest calculations involve exponents to determine the growth of an investment over time. Knowing how to work with exponents allows us to easily represent and manipulate very large or very small numbers, making complex calculations more manageable.
The given expression can be rewritten as 1 0 9 because the number 10 is multiplied 9 times. Therefore, the exponent is 9. The correct choice is C: 9.
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