Examine the expanded form:
[tex]$a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a$[/tex]
Which is the expression in exponential form?
A. [tex]$7^a$[/tex]
B. [tex]$7 a$[/tex]
C. [tex]$a^7$[/tex]
D. [tex]$a+7$[/tex]
Answer (2)
The expanded form is a c d o t a c d o t a c d o t a c d o t a c d o t a c d o t a .
Exponential form represents repeated multiplication.
a multiplied by itself 7 times is a 7 .
The expression in exponential form is a 7 .
Explanation
Understanding the Problem We are given the expanded form of an expression: a c d o t a c d o t a c d o t a c d o t a c d o t a c d o t a . Our goal is to identify the equivalent exponential form from the given options.
Converting to Exponential Form The expanded form shows 'a' multiplied by itself seven times. In exponential form, this is represented as a 7 , where 'a' is the base and 7 is the exponent.
Evaluating the Options Now, let's examine the given options:
7 a : This represents 7 raised to the power of 'a', which is not the same as 'a' multiplied by itself seven times.
7 a : This represents 7 times 'a', which is a linear expression, not an exponential one.
a 7 : This represents 'a' raised to the power of 7, which is 'a' multiplied by itself seven times. This matches the given expanded form.
a + 7 : This represents 'a' plus 7, which is a simple addition and not an exponential expression.
Final Answer Therefore, the correct exponential form of a c d o t a c d o t a c d o t a c d o t a c d o t a c d o t a is a 7 .
Examples
Exponential notation is used in many areas of science and engineering. For example, in computer science, 2 10 represents 1024, which is a common unit of memory (1 kilobyte). Similarly, in physics, scientific notation (e.g., 6.022 c d o t 1 0 23 ) uses exponents to represent very large or very small numbers in a compact and understandable format. Understanding exponential notation helps simplify complex calculations and express quantities efficiently.
The expanded form a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a can be expressed in exponential form as a 7 , since it represents 'a' multiplied by itself seven times. The correct choice from the options given is C. a 7 .
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