$3^8
\div 3^{-2}=$
A. $1^{-4}$
B. $6^6$
C. $3^{10}$
D. $3^{-4}$
Answer (1)
Apply the rule of exponents for division: a m o b re ak ÷ a n = a m − n .
Simplify the expression: 3 8 o b re ak ÷ 3 − 2 = 3 8 − ( − 2 ) = 3 8 + 2 = 3 10 .
Compare the result with the given options.
The correct answer is 3 10 .
Explanation
Understanding the problem We are given the expression 3 8 o b re ak ÷ 3 − 2 and asked to simplify it. We need to use the properties of exponents to simplify the expression and determine the correct answer from the given options.
Applying the exponent rule To simplify the expression, we use the rule for dividing exponential terms with the same base: a m o b re ak ÷ a n = a m − n . In our case, a = 3 , m = 8 , and n = − 2 . Applying this rule, we have: 3 8 o b re ak ÷ 3 − 2 = 3 8 − ( − 2 )
Simplifying the exponent Now, we simplify the exponent: 3 8 − ( − 2 ) = 3 8 + 2 = 3 10
Comparing with the options The simplified expression is 3 10 . Now we compare this result with the given options: A) 1 − 4 = 1 B) 6 6 = 46656 C) 3 10 = 59049 D) 3 − 4 = o b re ak 81 1 E) None of these
We see that option C, 3 10 , matches our simplified expression.
Final Answer Therefore, the correct answer is 3 10 .
Examples
Understanding exponents is crucial in many fields, such as computer science when dealing with binary numbers and data storage, or in finance when calculating compound interest. For example, if a bacteria population triples every hour, the population after 10 hours can be modeled as 3 10 times the initial population. This concept helps predict growth and make informed decisions.
