Select the correct product of the exponential expression. [tex]$6^4$[/tex]
A. [tex]$4 \cdot 6$[/tex]
B. 24
C. [tex]$4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$[/tex]
D. [tex]$6 \cdot 6 \cdot 6 \cdot 6$[/tex]
Answer (2)
The problem requires understanding the meaning of the exponential expression 6 4 .
6 4 means 6 multiplied by itself 4 times, which is 6 ⋅ 6 ⋅ 6 ⋅ 6 .
Comparing this with the given options, we find that option D is the correct one.
The correct product of the exponential expression 6 4 is 6 ⋅ 6 ⋅ 6 ⋅ 6 .
Explanation
Understanding the Problem The problem asks us to select the correct product of the exponential expression 6 4 from the given options.
Understanding Exponential Notation The expression 6 4 means 6 multiplied by itself 4 times, which can be written as 6 ⋅ 6 ⋅ 6 ⋅ 6 .
Comparing with Options Now, let's compare this with the given options:
Option A: 4 ⋅ 6 = 24 Option B: 24 Option C: 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 = 4 6 Option D: 6 ⋅ 6 ⋅ 6 ⋅ 6
We can see that Option D matches our understanding of 6 4 .
Final Answer Therefore, the correct product of the exponential expression 6 4 is 6 ⋅ 6 ⋅ 6 ⋅ 6 .
Examples
Exponential expressions are used in various real-life scenarios, such as calculating compound interest, population growth, and radioactive decay. For instance, if you invest money in a bank account with compound interest, the amount of money you have after a certain period can be calculated using an exponential expression. Similarly, the growth of a population or the decay of a radioactive substance can be modeled using exponential functions.
The correct product of the exponential expression 6 4 is 6 ⋅ 6 ⋅ 6 ⋅ 6 , which corresponds to Option D. This represents multiplying the number 6 by itself four times. Therefore, the answer is Option D.
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