Answer :
- Use the exponent rule: $x^a Imes x^b = x^{a+b}$.
- Apply the rule to the expression: $x^2 Imes x^3 = x^{2+3}$.
- Simplify the exponent: $x^{2+3} = x^5$.
- The correct answer is $\boxed{x^5}$.
### Explanation
1. Understanding the problem
We are given the expression $x^2 Imes x^3$ and asked to simplify it. We need to use the properties of exponents to simplify this expression.
2. Applying the exponent rule
To simplify the expression, we use the rule of exponents which states that when multiplying exponential expressions with the same base, we add the exponents: $x^a Imes x^b = x^{a+b}$.
3. Simplifying the expression
Applying this rule to our expression, we have $x^2 Imes x^3 = x^{2+3} = x^5$.
4. Finding the final answer
Therefore, the simplified expression is $x^5$. Comparing this to the given options, we see that option b) $x^5$ is the correct answer.
### Examples
Understanding exponent rules is crucial in many fields, such as computer science when dealing with data storage sizes (kilobytes, megabytes, gigabytes, etc.) or in physics when calculating quantities that scale exponentially, like radioactive decay or compound interest. For instance, if you're calculating the area of a square that grows exponentially each day, you'd use exponent rules to determine the area after a certain number of days. These rules provide a foundation for understanding growth and scaling in various real-world scenarios.
- Apply the rule to the expression: $x^2 Imes x^3 = x^{2+3}$.
- Simplify the exponent: $x^{2+3} = x^5$.
- The correct answer is $\boxed{x^5}$.
### Explanation
1. Understanding the problem
We are given the expression $x^2 Imes x^3$ and asked to simplify it. We need to use the properties of exponents to simplify this expression.
2. Applying the exponent rule
To simplify the expression, we use the rule of exponents which states that when multiplying exponential expressions with the same base, we add the exponents: $x^a Imes x^b = x^{a+b}$.
3. Simplifying the expression
Applying this rule to our expression, we have $x^2 Imes x^3 = x^{2+3} = x^5$.
4. Finding the final answer
Therefore, the simplified expression is $x^5$. Comparing this to the given options, we see that option b) $x^5$ is the correct answer.
### Examples
Understanding exponent rules is crucial in many fields, such as computer science when dealing with data storage sizes (kilobytes, megabytes, gigabytes, etc.) or in physics when calculating quantities that scale exponentially, like radioactive decay or compound interest. For instance, if you're calculating the area of a square that grows exponentially each day, you'd use exponent rules to determine the area after a certain number of days. These rules provide a foundation for understanding growth and scaling in various real-world scenarios.
