Simplify The Expression Below: $2^3 \times 2^2$A. $4^5$ B. $ 2 6 2^6 2 6 [/tex] C. $4^6$ D. $2^5$

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Understanding Exponents and Multiplication

When dealing with exponents, it's essential to understand the rules of multiplication. In this case, we have two terms with the same base ($2$) being multiplied together. According to the rules of exponents, when multiplying two terms with the same base, we add their exponents.

Applying the Rule of Exponents

The given expression is $2^3 \times 2^2$. Using the rule of exponents, we can simplify this expression by adding the exponents:

$$2^3 \times 2^2 = 2^{3+2} = 2^5$$

Evaluating the Simplified Expression

Now that we have simplified the expression to $2^5$, we can evaluate it. $2^5$ means $2$ multiplied by itself $5$ times:

$$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$$

Comparing with the Options

Let's compare our simplified expression ($2^5$) with the given options:

A. $4^5$ B. $2^6$ C. $4^6$ D. $2^5$

Our simplified expression ($2^5$) matches option D.

Conclusion

In conclusion, the simplified expression $2^3 \times 2^2$ is equal to $2^5$. This can be evaluated to $32$. Therefore, the correct answer is option D.

Frequently Asked Questions

• What is the rule of exponents for multiplication? The rule of exponents for multiplication states that when multiplying two terms with the same base, we add their exponents.
• How do we simplify the expression $2^3 \times 2^2$? We simplify the expression by adding the exponents: $2^3 \times 2^2 = 2^{3+2} = 2^5$.
• What is the value of $2^5$? $2^5$ is equal to $32$.

Additional Resources

• For more information on exponents and multiplication, visit Khan Academy's Exponents and Multiplication page.
• For practice problems and exercises, visit Mathway's Exponents and Multiplication page.

Final Answer

The final answer is $\boxed{D}$

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Frequently Asked Questions

Q: What is the rule of exponents for multiplication?

A: The rule of exponents for multiplication states that when multiplying two terms with the same base, we add their exponents.

Q: How do we simplify the expression $2^3 \times 2^2$?

A: We simplify the expression by adding the exponents: $2^3 \times 2^2 = 2^{3+2} = 2^5$.

Q: What is the value of $2^5$?

A: $2^5$ is equal to $32$.

Q: Can we simplify the expression $2^3 \times 2^2$ using a different method?

A: Yes, we can also simplify the expression by multiplying the numbers directly: $2^3 \times 2^2 = 8 \times 4 = 32$.

Q: What is the difference between $2^5$ and $4^5$?

A: $2^5$ is equal to $32$, while $4^5$ is equal to $1024$. They are two different numbers.

Q: Can we simplify the expression $2^3 \times 2^2$ using a calculator?

A: Yes, we can use a calculator to simplify the expression: $2^3 \times 2^2 = 8 \times 4 = 32$.

Q: What is the rule of exponents for division?

A: The rule of exponents for division states that when dividing two terms with the same base, we subtract their exponents.

Q: How do we simplify the expression $2^5 \div 2^2$?

A: We simplify the expression by subtracting the exponents: $2^5 \div 2^2 = 2^{5-2} = 2^3$.

Q: What is the value of $2^3$?

A: $2^3$ is equal to $8$.

More Questions and Answers

Q: What is the rule of exponents for negative exponents?

A: The rule of exponents for negative exponents states that $a^{-n} = \frac{1}{a^n}$.

Q: How do we simplify the expression $2^{-3}$?

A: We simplify the expression by using the rule of negative exponents: $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$.

Q: What is the rule of exponents for zero exponents?

A: The rule of exponents for zero exponents states that $a^0 = 1$.

Q: How do we simplify the expression $2^0$?

A: We simplify the expression by using the rule of zero exponents: $2^0 = 1$.

Conclusion

In conclusion, the rule of exponents for multiplication states that when multiplying two terms with the same base, we add their exponents. We can simplify the expression $2^3 \times 2^2$ by adding the exponents: $2^3 \times 2^2 = 2^{3+2} = 2^5$. The value of $2^5$ is equal to $32$. We can also simplify the expression using a different method or a calculator.

Frequently Asked Questions (FAQs)

• What is the rule of exponents for multiplication?
• How do we simplify the expression $2^3 \times 2^2$?
• What is the value of $2^5$?
• Can we simplify the expression $2^3 \times 2^2$ using a different method?
• What is the difference between $2^5$ and $4^5$?
• Can we simplify the expression $2^3 \times 2^2$ using a calculator?
• What is the rule of exponents for division?
• How do we simplify the expression $2^5 \div 2^2$?
• What is the value of $2^3$?
• What is the rule of exponents for negative exponents?
• How do we simplify the expression $2^{-3}$?
• What is the rule of exponents for zero exponents?
• How do we simplify the expression $2^0$?

Additional Resources

• For more information on exponents and multiplication, visit Khan Academy's Exponents and Multiplication page.
• For practice problems and exercises, visit Mathway's Exponents and Multiplication page.

Final Answer

The final answer is $\boxed{D}$