What is the exponential form of the following expression?
[tex]$(-5)(-5)(-5) \cdot c \cdot c \cdot c$[/tex]
A. [tex]$(-5) \cdot c^3$[/tex]
B. [tex]$(-5)^3 \cdot 3 c$[/tex]
C. [tex]$(-5)^3 \cdot c^3$[/tex]
D. [tex]$(-5) \cdot c^6$[/tex]
Answer (2)
Rewrite ( − 5 ) ( − 5 ) ( − 5 ) as ( − 5 ) 3 .
Rewrite c ⋅ c ⋅ c as c 3 .
Combine the terms to get ( − 5 ) 3 ⋅ c 3 .
The exponential form of the given expression is ( − 5 ) 3 ⋅ c 3 .
Explanation
Understanding the Problem We are asked to express the given expression in exponential form. The expression is ( − 5 ) ( − 5 ) ( − 5 ) ⋅ c ⋅ c ⋅ c .
Simplifying the Numerical Part First, let's simplify the numerical part of the expression. We have ( − 5 ) ( − 5 ) ( − 5 ) . This is the same as ( − 5 ) multiplied by itself three times, which can be written as ( − 5 ) 3 .
Simplifying the Variable Part Next, let's simplify the variable part of the expression. We have c ⋅ c ⋅ c . This is the same as c multiplied by itself three times, which can be written as c 3 .
Combining the Terms Now, let's combine the simplified numerical and variable parts. We have ( − 5 ) 3 and c 3 . Multiplying these together, we get ( − 5 ) 3 ⋅ c 3 .
Final Answer Therefore, the exponential form of the given expression is ( − 5 ) 3 ⋅ c 3 .
Examples
Exponential forms are used to represent repeated multiplication, which is very useful in calculating compound interest. For example, if you invest $100 at an annual interest rate of 5%, the amount you have after 3 years can be calculated as 100 ⋅ ( 1 + 0.05 ) 3 . Exponential forms also appear in physics, such as when calculating the decay of radioactive materials or the growth of populations.
The exponential form of the expression ( − 5 ) ( − 5 ) ( − 5 ) ⋅ c ⋅ c ⋅ c is ( − 5 ) 3 ⋅ c 3 . The correct answer choice is C. ( − 5 ) 3 ⋅ c 3 .
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