Write the quotient as an exponent: [tex]$c^{12} \div c^3$[/tex]
Answer (2)
Apply the quotient rule for exponents: $c^{12}
div c^3 = c^{12-3}$.
Subtract the exponents: 12 − 3 = 9 .
Write the final expression: c 9 .
The quotient as an exponent is c 9 .
Explanation
Understanding the Problem We are given the expression $c^{12}
div c^3$ and asked to write the quotient as an exponent.
Applying the Quotient Rule To simplify this expression, we will use the quotient rule for exponents, which states that when dividing exponential expressions with the same base, we subtract the exponents: a m d i v a n = a m − n
Simplifying the Exponent Applying this rule to our expression, we have: c 12 d i v c 3 = c 12 − 3
Final Result Now, we subtract the exponents: 12 − 3 = 9 So, the simplified expression is: c 9
Examples
Understanding exponents and their properties is crucial in various fields, such as calculating compound interest, where the exponent represents the number of compounding periods. For instance, if you invest money with an annual interest rate compounded quarterly, you need to understand how the exponent affects the final amount. Similarly, in physics, exponents are used to describe relationships like the inverse square law in gravitational force, where the force is inversely proportional to the square of the distance. These examples show how mastering exponents can help in real-world calculations and understanding complex phenomena.
To simplify the expression c 12 ÷ c 3 , we apply the quotient rule of exponents, which involves subtracting the exponents. This gives us c 12 − 3 = c 9 . The final result is c 9 .
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