Problem Analysis:
The task involves simplifying exponential expressions. The rules of exponents are essential for solving these problems. Here are the key rules we will use:
1.
Product Rule: $ a^m \cdot a^n = a^{m+n} $
2.
Quotient Rule: $ \frac{a^m}{a^n} = a^{m-n} $
3.
Power Rule: $ (a^m)^n = a^{m \cdot n} $
Let's solve each problem step by step.
---
Problem 1: Simplify the expression $ x^4 \cdot x^5 $
#### Solution:
Using the
Product Rule ($ a^m \cdot a^n = a^{m+n} $):
$$
x^4 \cdot x^5 = x^{4+5} = x^9
$$
#### Correct Answer:
$$
\boxed{\text{b) } x^9}
$$
---
Problem 2: Simplify the expression $ y^{10} \div y^7 $
#### Solution:
Using the
Quotient Rule ($ \frac{a^m}{a^n} = a^{m-n} $):
$$
y^{10} \div y^7 = y^{10-7} = y^3
$$
#### Correct Answer:
$$
\boxed{\text{c) } y^3}
$$
---
Problem 3: Simplify the expression $ g^3 \cdot g^4 $
#### Solution:
Using the
Product Rule ($ a^m \cdot a^n = a^{m+n} $):
$$
g^3 \cdot g^4 = g^{3+4} = g^7
$$
#### Correct Answer:
$$
\boxed{\text{d) } g^7}
$$
---
Problem 4: Simplify the expression $ y^7 \cdot y^2 $
#### Solution:
Using the
Product Rule ($ a^m \cdot a^n = a^{m+n} $):
$$
y^7 \cdot y^2 = y^{7+2} = y^9
$$
#### Correct Answer:
$$
\boxed{\text{b) } y^9}
$$
---
Final Answers:
1. $ \boxed{\text{b) } x^9} $
2. $ \boxed{\text{c) } y^3} $
3. $ \boxed{\text{d) } g^7} $
4. $ \boxed{\text{b) } y^9} $
These solutions are derived using the fundamental rules of exponents, ensuring accuracy and clarity.
Parent Tip: Review the logic above to help your child master the concept of property of exponents worksheet.
