Which Of These Is Equal To 5 0 + 2 1 5^0 + 2^1 5 0 + 2 1 ?A. ( 3 + 5 ) × ( 5 + 3 + 6 (3+5) \times (5+3+6 ( 3 + 5 ) × ( 5 + 3 + 6 ] B. ( 3 × 5 ) + ( 5 + 3 + 6 (3 \times 5) + (5+3+6 ( 3 × 5 ) + ( 5 + 3 + 6 ] C. ( 3 + 5 ) + ( 5 × 3 × 6 (3+5) + (5 \times 3 \times 6 ( 3 + 5 ) + ( 5 × 3 × 6 ] D. ( 3 × 5 ) × ( 5 + 3 + 6 (3 \times 5) \times (5+3+6 ( 3 × 5 ) × ( 5 + 3 + 6 ]

Understanding Exponents and Basic Arithmetic Operations

In mathematics, exponents are a fundamental concept used to represent repeated multiplication of a number. The expression $5^0$ means 5 multiplied by itself zero times, which is equal to 1. Similarly, $2^1$ means 2 multiplied by itself one time, which is equal to 2. When we add these two expressions together, we get $5^0 + 2^1 = 1 + 2 = 3$.

Evaluating the Options

Now, let's evaluate the given options to determine which one is equal to $5^0 + 2^1$.

Option A: $(3+5) \times (5+3+6$

To evaluate this option, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses: $(3+5) = 8$ and $(5+3+6) = 14$
2. Multiply the two results: $8 \times 14 = 112$

This option is not equal to $5^0 + 2^1$.

Option B: $(3 \times 5) + (5+3+6$

To evaluate this option, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses: $(3 \times 5) = 15$ and $(5+3+6) = 14$
2. Add the two results: $15 + 14 = 29$

This option is not equal to $5^0 + 2^1$.

Option C: $(3+5) + (5 \times 3 \times 6$

To evaluate this option, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses: $(3+5) = 8$ and $(5 \times 3 \times 6) = 90$
2. Add the two results: $8 + 90 = 98$

This option is not equal to $5^0 + 2^1$.

Option D: $(3 \times 5) \times (5+3+6$

To evaluate this option, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses: $(3 \times 5) = 15$ and $(5+3+6) = 14$
2. Multiply the two results: $15 \times 14 = 210$

This option is not equal to $5^0 + 2^1$.

Conclusion

None of the given options are equal to $5^0 + 2^1$. The correct answer is not among the options provided. However, we can see that the correct answer is simply the sum of $5^0$ and $2^1$, which is equal to 3.

Tips and Tricks

When evaluating expressions with exponents and basic arithmetic operations, it's essential to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate exponents next (e.g., $5^0$).
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate addition and subtraction operations from left to right.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate exponents next (e.g., $5^0$).
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate addition and subtraction operations from left to right.

Q: How do I evaluate expressions with exponents?

A: To evaluate expressions with exponents, you need to follow the order of operations (PEMDAS). Here's a step-by-step guide:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponents (e.g., $5^0$).
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between $5^0$ and $5^1$?

A: $5^0$ means 5 multiplied by itself zero times, which is equal to 1. $5^1$ means 5 multiplied by itself one time, which is equal to 5.

Q: How do I simplify expressions with multiple operations?

A: To simplify expressions with multiple operations, you need to follow the order of operations (PEMDAS). Here's a step-by-step guide:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponents (e.g., $5^0$).
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the value of $2^3 + 5^2$?

A: To evaluate this expression, you need to follow the order of operations (PEMDAS):

1. Evaluate the exponents: $2^3 = 8$ and $5^2 = 25$
2. Add the two results: $8 + 25 = 33$

Therefore, the value of $2^3 + 5^2$ is 33.

Q: How do I evaluate expressions with negative exponents?

A: To evaluate expressions with negative exponents, you need to follow the rule that $a^{-n} = \frac{1}{a^n}$. For example, $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$.

Q: What is the value of $3^{-2} + 2^3$?

A: To evaluate this expression, you need to follow the order of operations (PEMDAS):

1. Evaluate the exponents: $3^{-2} = \frac{1}{3^2} = \frac{1}{9}$ and $2^3 = 8$
2. Add the two results: $\frac{1}{9} + 8 = \frac{1}{9} + \frac{72}{9} = \frac{73}{9}$

Therefore, the value of $3^{-2} + 2^3$ is $\frac{73}{9}$.

Conclusion

In this article, we've covered some common questions and topics related to exponents and basic arithmetic operations. We've discussed the order of operations (PEMDAS), how to evaluate expressions with exponents, and how to simplify expressions with multiple operations. We've also provided examples and practice problems to help you understand these concepts better.