Solve the Expression: Finding 7^1 - 7^2

Q: Do I need to follow order of operations here?

Yes, absolutely! Remember PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Since exponents come before subtraction, calculate $ 7^1 $ and $ 7^2 $ first, then subtract.

Q: What does 7^1 equal and why?

Any number raised to the power of 1 equals itself. So $ 7^1 = 7 $. This is because you're multiplying the base by itself 1 time, which is just the number itself!

Q: How do I calculate 7^2 without a calculator?

$ 7^2 $ means 7 × 7. You can break it down: $ 7 \times 7 = (5 + 2) \times 7 = 35 + 14 = 49 $. Practice your multiplication tables to make this faster!

Q: Could the answer be positive instead?

No, the answer must be negative. Since we're calculating $ 7 - 49 $, we're subtracting 49 from 7. This always gives -42, not +42. The order matters in subtraction!

Exponent Evaluation with Negative Results

Solve the following exercise:

$7^1-7^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following expression

00:04 Break down the exponents

00:12 Always solve multiplication and division before addition and subtraction

00:19 Continue to solve the expression according to the correct order of operations, from left to right

00:23 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$7^1-7^2=$

Step-by-step solution

To solve the expression $7^1 - 7^2$ , we need to evaluate the powers first before performing the subtraction. The steps are as follows:

Calculate $7^1$ : Since any number to the power of 1 is the number itself, we have $7^1 = 7$ .
Calculate $7^2$ : This means 7 is multiplied by itself, which gives us $7 \times 7 = 49$ .
Subtract the results: Now, perform the subtraction $7 - 49$ .
This yields: $7 - 49 = -42$ .

Thus, the correct answer is $-42$ .

Final Answer

$-42$

Key Points to Remember

Essential concepts to master this topic

Rule: Always calculate exponents before performing subtraction operations
Technique: Evaluate $7^1 = 7$ and $7^2 = 49$ first
Check: Substitute back: $7 - 49 = -42$ matches our answer ✓

Common Mistakes

Avoid these frequent errors

Performing subtraction before evaluating exponents
Don't subtract the exponents like 7^(1-2) = 7^(-1) = 1/7! This ignores order of operations and gives a completely wrong result. Always evaluate each exponent first, then perform the subtraction operation.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

Why is the answer negative when both numbers are positive?

Great question! Even though 7 is positive, we're subtracting a larger number (49) from a smaller one (7). Whenever you subtract a larger number from a smaller one, the result is negative: $7 - 49 = -42$ .

Do I need to follow order of operations here?

Yes, absolutely! Remember PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Since exponents come before subtraction, calculate $7^1$ and $7^2$ first, then subtract.

What does 7^1 equal and why?

Any number raised to the power of 1 equals itself. So $7^1 = 7$ . This is because you're multiplying the base by itself 1 time, which is just the number itself!

How do I calculate 7^2 without a calculator?

$7^2$ means 7 × 7. You can break it down: $7 \times 7 = (5 + 2) \times 7 = 35 + 14 = 49$ . Practice your multiplication tables to make this faster!

Could the answer be positive instead?

No, the answer must be negative. Since we're calculating $7 - 49$ , we're subtracting 49 from 7. This always gives -42, not +42. The order matters in subtraction!

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Solve the Expression: Finding 7^1 - 7^2

Exponent Evaluation with Negative Results

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the answer negative when both numbers are positive?

Do I need to follow order of operations here?

What does 7^1 equal and why?

How do I calculate 7^2 without a calculator?

Could the answer be positive instead?

🌟 Unlock Your Math Potential

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