Find the value of the expression: [tex]$2.73^{13} \div 2.73^{12}$[/tex]
Answer (2)
Apply the quotient of powers property: a m / a n = a m − n .
Substitute the given values: 2.7 3 13 /2.7 3 12 = 2.7 3 13 − 12 .
Simplify the exponent: 13 − 12 = 1 .
The expression simplifies to: 2.7 3 1 = 2.73 , so the final answer is 2.73 .
Explanation
Understanding the Problem We are asked to find the value of the expression 2.7 3 13 ÷ 2.7 3 12 . This involves dividing two exponential terms with the same base.
Applying the Quotient of Powers Property To solve this, we will use the quotient of powers property, which states that when dividing exponential terms with the same base, we subtract the exponents: a m ÷ a n = a m − n
Substituting the Values In our case, the base is 2.73, and the exponents are 13 and 12. Applying the property, we get: 2.7 3 13 ÷ 2.7 3 12 = 2.7 3 13 − 12
Simplifying the Exponent Now, we simplify the exponent: 13 − 12 = 1 So, the expression becomes: 2.7 3 1
Final Result Any number raised to the power of 1 is simply the number itself. Therefore: 2.7 3 1 = 2.73
Examples
Exponential expressions are useful in calculating compound interest. For example, if you invest money in a bank account that pays compound interest, the amount of money you have after a certain number of years can be calculated using an exponential expression. Understanding how to simplify exponential expressions can help you to easily calculate the returns on your investments.
The expression 2.7 3 13 ÷ 2.7 3 12 simplifies to 2.73 by applying the quotient of powers property. By subtracting the exponents, we determine the result is simply the base raised to the power of 1. Thus, the final answer is 2.73 .
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