Solve -(-2)^4+(-2)^2: Order of Operations with Negative Exponents

Q: Why does $(-2)^4$ equal positive 16?

When you raise a negative number to an even exponent, the result is always positive! $(-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16$ because negative times negative equals positive.

Q: What's the difference between $-(-2)^4$ and $(-(-2))^4$ ?

The placement of parentheses matters! $-(-2)^4 = -(16) = -16$ because you apply the exponent first, then negate. But $(-(-2))^4 = (2)^4 = 16$ because you negate first, then apply the exponent.

Q: How do I remember the order of operations here?

Use PEMDAS! Exponents come before subtraction/negation. So calculate $(-2)^4$ first to get 16, then apply the negative sign to get -16.

Q: Why is $(-2)^2$ positive but $-(-2)^4$ negative?

$(-2)^2 = 4$ is positive because any number to an even power is positive. But $-(-2)^4 = -16$ is negative because of the extra minus sign in front that negates the positive result!

Q: Can I just ignore the parentheses around -2?

Never ignore parentheses! They show that the entire number -2 is being raised to the power. Without them, $-2^4 = -(2^4) = -16$, which is different from $(-2)^4 = 16$.

Exponent Rules with Negative Bases

$-(-2)^4+(-2)^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 First let's calculate the sign

00:08 Even power, therefore the sign will be positive

00:27 Let's calculate the powers

00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-(-2)^4+(-2)^2=$

Step-by-step solution

To solve this problem, let's evaluate the expression $-(-2)^4 + (-2)^2$ step-by-step:

Step 1: Calculate $(-2)^4$ .
Since the exponent is even, $(-2)^4 = ((-2) \times (-2) \times (-2) \times (-2))$ .
Calculating more explicitly:
$(-2) \times (-2) = 4$ ,
$4 \times (-2) = -8$ ,
$-8 \times (-2) = 16$ .
Thus, $(-2)^4 = 16$ .
Step 2: Negate the result from step 1.
$-(-2)^4 = -(16) = -16$ .
Step 3: Calculate $(-2)^2$ .
Since the exponent is even, $(-2)^2 = (-2) \times (-2) = 4$ .
Step 4: Add the results from step 2 and step 3.
$-16 + 4 = -12$ .

Therefore, the final result is $\mathbf{-12}$ .

Final Answer

$-12$

Key Points to Remember

Essential concepts to master this topic

Rule: Apply exponents before negation signs for order of operations
Technique: $(-2)^4 = 16$ , then $-(-2)^4 = -16$
Check: Verify each step: $-16 + 4 = -12$ matches the correct answer ✓

Common Mistakes

Avoid these frequent errors

Applying negation before calculating exponents
Don't calculate $-(-2)^4$ as $(2)^4 = 16$ ! This ignores order of operations and gives a positive result instead of negative. Always calculate exponents first, then apply the negation sign outside.

Practice Quiz

Test your knowledge with interactive questions

Solve the following expression:

$$ $$ (-8)^2= $$

FAQ

Everything you need to know about this question

Why does $(-2)^4$ equal positive 16?

When you raise a negative number to an even exponent, the result is always positive! $(-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16$ because negative times negative equals positive.

What's the difference between $-(-2)^4$ and $(-(-2))^4$ ?

The placement of parentheses matters! $-(-2)^4 = -(16) = -16$ because you apply the exponent first, then negate. But $(-(-2))^4 = (2)^4 = 16$ because you negate first, then apply the exponent.

How do I remember the order of operations here?

Use PEMDAS! Exponents come before subtraction/negation. So calculate $(-2)^4$ first to get 16, then apply the negative sign to get -16.

Why is $(-2)^2$ positive but $-(-2)^4$ negative?

$(-2)^2 = 4$ is positive because any number to an even power is positive. But $-(-2)^4 = -16$ is negative because of the extra minus sign in front that negates the positive result!

Can I just ignore the parentheses around -2?

Never ignore parentheses! They show that the entire number -2 is being raised to the power. Without them, $-2^4 = -(2^4) = -16$ , which is different from $(-2)^4 = 16$ .

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Solve -(-2)^4+(-2)^2: Order of Operations with Negative Exponents

Exponent Rules with Negative Bases

❤️ 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 does $(-2)^4$ equal positive 16?

What's the difference between $-(-2)^4$ and $(-(-2))^4$ ?

How do I remember the order of operations here?

Why is $(-2)^2$ positive but $-(-2)^4$ negative?

Can I just ignore the parentheses around -2?

🌟 Unlock Your Math Potential

More Questions

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Solve -(-2)^4+(-2)^2: Order of Operations with Negative Exponents

Exponent Rules with Negative Bases

❤️ 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 does (−2)4(-2)^4(−2)4 equal positive 16?

What's the difference between −(−2)4-(-2)^4−(−2)4 and (−(−2))4(-(-2))^4(−(−2))4?

How do I remember the order of operations here?

Why is (−2)2(-2)^2(−2)2 positive but −(−2)4-(-2)^4−(−2)4 negative?

Can I just ignore the parentheses around -2?

🌟 Unlock Your Math Potential

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Why does $(-2)^4$ equal positive 16?

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Why is $(-2)^2$ positive but $-(-2)^4$ negative?