algebra 1 ab
unit 7 exponents and exponential functions
lesson 1 warm - up terms, expressions, and coefficients
name: adrianna
1/23/26
1. simplify each of the expressions as far as possible:
a. $4x^{2}+7x^{2}$
b. $2x + 3y$
c. $m^{2}+m^{2}+m^{2}$
d. $3y^{2}+2y^{3}$
2. write the following using exponents:
a. $t\bullet t\bullet t\bullet t$
b. $y\bullet y + y\bullet y$
3. write the following without using exponents or coefficients (reverse problem no. 2):
a. $x^{3}$
b. $m^{2}n^{4}$
c. $4p$
4. evaluate the following:
a. $3^{4}$
b. $2\bullet5^{2}$
5. identify (by labeling) the exponent, base and coefficient in the expression below:
$3x^{2}$

Question

algebra 1 ab
unit 7 exponents and exponential functions
lesson 1 warm - up terms, expressions, and coefficients
name: adrianna
1/23/26
1. simplify each of the expressions as far as possible:
   a. $4x^{2}+7x^{2}$
   b. $2x + 3y$
   c. $m^{2}+m^{2}+m^{2}$
   d. $3y^{2}+2y^{3}$
2. write the following using exponents:
   a. $t\bullet t\bullet t\bullet t$
   b. $y\bullet y + y\bullet y$
3. write the following without using exponents or coefficients (reverse problem no. 2):
   a. $x^{3}$
   b. $m^{2}n^{4}$
   c. $4p$
4. evaluate the following:
   a. $3^{4}$
   b. $2\bullet5^{2}$
5. identify (by labeling) the exponent, base and coefficient in the expression below:
   $3x^{2}$

Accepted Answer

### Question 1a: Simplify $ 4x^2 + 7x^2 $
# Explanation:
## Step 1: Identify like terms
Both terms have $ x^2 $, so they are like terms.
## Step 2: Combine coefficients
Add the coefficients $ 4 $ and $ 7 $: $ 4 + 7 = 11 $.
## Step 3: Write the simplified term
Multiply the sum of coefficients by $ x^2 $: $ 11x^2 $.
# Answer: $ 11x^2 $

### Question 1b: Simplify $ 2x + 3y $
# Explanation:
## Step 1: Check for like terms
$ 2x $ has variable $ x $, $ 3y $ has variable $ y $. Different variables, so no like terms.
## Step 2: Conclusion
The expression cannot be simplified further.
# Answer: $ 2x + 3y $

### Question 1c: Simplify $ m^2 + m^2 + m^2 $
# Explanation:
## Step 1: Identify like terms
All terms have $ m^2 $, so they are like terms.
## Step 2: Combine coefficients
Add the coefficients $ 1 + 1 + 1 = 3 $ (each $ m^2 $ has coefficient 1).
## Step 3: Write the simplified term
Multiply the sum of coefficients by $ m^2 $: $ 3m^2 $.
# Answer: $ 3m^2 $

### Question 1d: Simplify $ 3y^2 + 2y^3 $
# Explanation:
## Step 1: Check for like terms
$ 3y^2 $ has exponent 2, $ 2y^3 $ has exponent 3. Different exponents, so no like terms.
## Step 2: Conclusion
The expression cannot be simplified further.
# Answer: $ 3y^2 + 2y^3 $

### Question 2a: Write $ t \cdot t \cdot t \cdot t $ using exponents
# Explanation:
## Step 1: Recall exponent definition
$ a \cdot a \cdot \dots \cdot a $ (n times) is $ a^n $. Here, $ t $ is multiplied 4 times.
## Step 2: Apply the definition
$ t \cdot t \cdot t \cdot t = t^4 $.
# Answer: $ t^4 $

### Question 2b: Write $ y \cdot y + y \cdot y $ using exponents
# Explanation:
## Step 1: Simplify each product
$ y \cdot y = y^2 $, so we have $ y^2 + y^2 $.
## Step 2: Combine like terms
Add the coefficients: $ 1 + 1 = 2 $, so $ 2y^2 $.
# Answer: $ 2y^2 $

### Question 3a: Write $ x^3 $ without exponents
# Explanation:
## Step 1: Recall exponent meaning
$ x^3 = x \cdot x \cdot x $ (3 times multiplication).
## Step 2: Write the expansion
$ x \cdot x \cdot x $.
# Answer: $ x \cdot x \cdot x $

### Question 3b: Write $ m^2n^4 $ without exponents
# Explanation:
## Step 1: Expand $ m^2 $
$ m^2 = m \cdot m $.
## Step 2: Expand $ n^4 $
$ n^4 = n \cdot n \cdot n \cdot n $.
## Step 3: Combine the expansions
$ m \cdot m \cdot n \cdot n \cdot n \cdot n $.
# Answer: $ m \cdot m \cdot n \cdot n \cdot n \cdot n $

### Question 3c: Write $ 4p $ without coefficients
# Explanation:
## Step 1: Recall coefficient meaning
$ 4p = p + p + p + p $ (4 times addition of $ p $).
## Step 2: Write the expansion
$ p + p + p + p $.
# Answer: $ p + p + p + p $

### Question 4a: Evaluate $ 3^4 $
# Explanation:
## Step 1: Recall exponent definition
$ 3^4 = 3 \cdot 3 \cdot 3 \cdot 3 $.
## Step 2: Calculate the product
$ 3 \cdot 3 = 9 $, $ 9 \cdot 3 = 27 $, $ 27 \cdot 3 = 81 $.
# Answer: $ 81 $

### Question 4b: Evaluate $ 2 \cdot 5^2 $
# Explanation:
## Step 1: Evaluate the exponent first
$ 5^2 = 5 \cdot 5 = 25 $.
## Step 2: Multiply by 2
$ 2 \cdot 25 = 50 $.
# Answer: $ 50 $

### Question 5: Identify exponent, base, coefficient in $ 3x^2 $
# Explanation:
## Step 1: Recall definitions
- Coefficient: The numerical factor (3).
- Base: The variable being raised to a power (x).
- Exponent: The power to which the base is raised (2).
## Step 2: Label each part
- Coefficient: 3
- Base: x
- Exponent: 2
# Answer:
- Coefficient: $ 3 $
- Base: $ x $
- Exponent: $ 2 $

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QUESTION IMAGE

Question

Explanation:

Question 1a: Simplify \( 4x^2 + 7x^2 \)

Step 1: Identify like terms

Step 2: Combine coefficients

Step 3: Write the simplified term

Step 1: Check for like terms

Step 2: Conclusion

Step 1: Identify like terms

Step 2: Combine coefficients

Step 3: Write the simplified term

Answer:

Question 1b: Simplify \( 2x + 3y \)