Question

1. write ( 7 cdot 7 cdot 7 cdot 7 ) by using exponential notation.

1. write ( 4^3 ) in expanded form.

1. which expression is equivalent to ( 5^6 )?

a. ( 5 cdot 6 )
b. ( 5 cdot 5 )
c. ( 5 cdot 5 cdot 5 cdot 5 cdot 5 cdot 5 )
d. ( 5 + 5 + 5 + 5 + 5 + 5 )
e. ( 6 cdot 6 cdot 6 cdot 6 cdot 6 )

1. kayla says that ( 2^3 ) and ( 2 cdot 3 ) are equivalent expressions. is kayla correct? explain.

Explanation:

Question 2

Step1: Recall exponential notation

Exponential notation \(a^n\) means \(a\) multiplied by itself \(n\) times, where \(a\) is the base and \(n\) is the exponent.
Here, we have \(7\cdot7\cdot7\cdot7\), which is 7 multiplied by itself 4 times.

Step2: Write in exponential notation

So, \(7\cdot7\cdot7\cdot7 = 7^4\).

Step1: Recall expanded form of exponents

The exponential form \(a^n\) in expanded form is \(a\) multiplied by itself \(n\) times.
For \(4^3\), the base \(a = 4\) and the exponent \(n = 3\).

Step2: Expand the exponent

This means \(4^3=4\cdot4\cdot4\).

Step1: Recall the meaning of exponential notation

\(a^n\) means \(a\) multiplied by itself \(n\) times. For \(5^6\), the base is 5 and the exponent is 6.

Step2: Analyze each option

• Option A: \(5\cdot6\) is 5 times 6, not 5 to the power of 6. Incorrect.
• Option B: \(5\cdot5\) is \(5^2\), not \(5^6\). Incorrect.
• Option C: \(5\cdot5\cdot5\cdot5\cdot5\cdot5\) is 5 multiplied by itself 6 times, which is \(5^6\). Correct.
• Option D: \(5 + 5+5+5+5+5\) is addition, not multiplication. Incorrect.
• Option E: \(6\cdot6\cdot6\cdot6\cdot6\) is \(6^5\), not \(5^6\). Incorrect.

Answer:

\(7^4\)

Question 3