1. consider (2^5)
a. identify the base.
b. identify the exponent.
c. write in words how (2^5) is read aloud.
d. explain how to evaluate (2^5).
2. write (7 cdot 7 cdot 7 cdot 7) by using exponential notation.
3. write (a^4) in expanded form.
4. 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)
5. kayla says that (2^3) and (3^2) are equivalent expressions. is kayla correct? explain.

Question

1. consider (2^5)
 a. identify the base.
 b. identify the exponent.
 c. write in words how (2^5) is read aloud.
 d. explain how to evaluate (2^5).
 2. write (7 cdot 7 cdot 7 cdot 7) by using exponential notation.
 3. write (a^4) in expanded form.
 4. 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)
 5. kayla says that (2^3) and (3^2) are equivalent expressions. is kayla correct? explain.

Accepted Answer

### Question 1:
#### a. Identify the base.
# Brief Explanations:
In an exponential expression $a^n$, $a$ is the base. For $2^5$, the base is the number being raised to a power.
# Answer:
The base of $2^5$ is $2$.

#### b. Identify the exponent.
# Brief Explanations:
In $a^n$, $n$ is the exponent, representing how many times the base is multiplied by itself. For $2^5$, the exponent is the superscript.
# Answer:
The exponent of $2^5$ is $5$.

#### c. Write in words how $2^5$ is read aloud.
# Brief Explanations:
Exponential notation $a^n$ is read as "a raised to the power of n" or "a to the nth power". For $2^5$, we apply this.
# Answer:
$2^5$ is read as "2 raised to the power of 5" or "2 to the 5th power".

#### d. Explain how to evaluate $2^5$.
# Explanation:
## Step1: Recall exponent definition
An exponent $n$ on a base $a$ means multiplying $a$ by itself $n$ times. So $a^n=\underbrace{a\times a\times\cdots\times a}_{n\text{ times}}$.
## Step2: Apply to $2^5$
For $2^5$, base $a = 2$, exponent $n=5$. So $2^5=2\times2\times2\times2\times2$.
## Step3: Calculate the product
$2\times2 = 4$, $4\times2=8$, $8\times2 = 16$, $16\times2=32$.
# Answer:
To evaluate $2^5$, we multiply the base $2$ by itself 5 times: $2\times2\times2\times2\times2 = 32$.

### Question 2: Write $7\cdot7\cdot7\cdot7$ using exponential notation.
# Explanation:
## Step1: Identify base and exponent
The base $a$ is the number being multiplied repeatedly, here $a = 7$. The number of times $7$ is multiplied is the exponent $n$. Since $7$ is multiplied 4 times, $n = 4$.
## Step2: Write in exponential form
Exponential form is $a^n$, so substituting $a = 7$ and $n = 4$, we get $7^4$.
# Answer:
$7\cdot7\cdot7\cdot7$ in exponential notation is $7^4$.

### Question 3: Write $a^4$ in expanded form.
# Explanation:
## Step1: Recall exponent definition
For $a^n$, expanded form is multiplying $a$ by itself $n$ times. Here $n = 4$ and base $a$.
## Step2: Write the expansion
So $a^4=a\times a\times a\times a$.
# Answer:
The expanded form of $a^4$ is $a\times a\times a\times a$.

### Question 4: Which expression is equivalent to $5^6$?
# Brief Explanations:
$5^6$ means multiplying $5$ by itself 6 times (by the definition of exponents: $a^n=\underbrace{a\times a\times\cdots\times a}_{n\text{ times}}$). Let's analyze each option:
- Option A: $5\cdot6$ is $5\times6$, not repeated multiplication of $5$. Eliminate.
- Option B: $5\cdot5$ is $5^2$, only 2 multiplications. Eliminate.
- Option C: $5\cdot5\cdot5\cdot5\cdot5\cdot5$ is $5$ multiplied 6 times, which matches $5^6$ (since $n = 6$, 6 factors of $5$).
- Option D: $5 + 5+5+5+5+5$ is addition, not multiplication. Eliminate.
- Option E: $6\cdot6\cdot6\cdot6$ is $6^4$, base 6. Eliminate.
# Answer:
C. $5\cdot5\cdot5\cdot5\cdot5\cdot5$

### Question 5: Kayla says that $2^3$ and $3^2$ are equivalent expressions. Is Kayla correct? Explain.
# Explanation:
## Step1: Evaluate $2^3$
By exponent definition, $2^3=2\times2\times2$. Calculating: $2\times2 = 4$, $4\times2=8$.
## Step2: Evaluate $3^2$
$3^2=3\times3 = 9$.
## Step3: Compare results
Since $8
eq9$, $2^3$ and $3^2$ are not equal.
# Answer:
Kayla is not correct. $2^3 = 2\times2\times2=8$ and $3^2=3\times3 = 9$. Since $8
eq9$, the two expressions are not equivalent.

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QUESTION IMAGE

Question

Explanation:

Question 1:

a. Identify the base.

Answer:

b. Identify the exponent.