$10^8 \div 10^4=$
F $\quad 1^4$
G $\quad 10^2$
H $10^{12}$
J $100^4$
K None of these
Answer (1)
Apply the exponent division rule: 1 0 8 ÷ 1 0 4 = 1 0 8 − 4 .
Simplify the exponent: 1 0 8 − 4 = 1 0 4 .
Evaluate 1 0 4 : 1 0 4 = 10 , 000 .
Compare the result with the given options and conclude that the correct answer is None of these .
Explanation
Understanding the problem We are given the expression 1 0 8 ÷ 1 0 4 and asked to simplify it. We need to use the properties of exponents to simplify this expression and determine which of the given options is correct.
Applying the exponent rule To simplify the expression, we use the rule for dividing exponential terms with the same base: a m ÷ a n = a m − n . In our case, the base is 10, m = 8 , and n = 4 . Applying this rule, we get:
1 0 8 ÷ 1 0 4 = 1 0 8 − 4 = 1 0 4
Evaluating the exponent Now we need to evaluate 1 0 4 . This means 10 multiplied by itself 4 times:
1 0 4 = 10 × 10 × 10 × 10 = 10 , 000
Comparing with the options Now, let's examine the given options to see which one matches our result of 1 0 4 = 10 , 000 :
F: 1 4 = 1
G: 1 0 2 = 100
H: 1 0 12 = 1 , 000 , 000 , 000 , 000
J: 10 0 4 = ( 1 0 2 ) 4 = 1 0 8 = 100 , 000 , 000
K: None of these
None of the given options match our result of 1 0 4 = 10 , 000 .
Final Answer Since none of the provided options match the simplified expression, the correct answer is:
K: None of these
Examples
Understanding exponents is crucial in many real-world applications. For instance, in computer science, memory sizes are often expressed in powers of 2 (e.g., kilobytes, megabytes, gigabytes). Similarly, exponential growth and decay models are used in finance to calculate compound interest or depreciation. Simplifying expressions with exponents allows us to easily compare and understand these quantities.
