Calculate the Absolute Value: Solving |-2 Cubed|

Q: Why is $(-2)^3$ negative when we're multiplying negative numbers?

When you multiply an odd number of negative factors, the result is negative. Here we have three negative twos: $-2 \times -2 \times -2$, so the answer is $-8$.

Q: What's the difference between $(-2)^3$ and $-2^3$ ?

$(-2)^3 = -8$ because the parentheses include the negative sign in the base. But $-2^3 = -(2^3) = -8$ means negative of 2 cubed. In this case, both equal -8, but they can differ with even exponents!

Q: Does absolute value always make numbers positive?

Yes! The absolute value of any real number is always non-negative. $|8| = 8$ and $|-8| = 8$. Think of it as the distance from zero on a number line.

Q: How do I remember the order of operations with absolute value?

Use PEMDAS! Absolute value bars act like parentheses, so calculate everything inside them first. Only after you get the result inside do you apply the absolute value operation.

Q: What if I calculated $2^3 = 8$ instead?

That's a common mistake! You must keep the negative sign as part of the base when it's in parentheses. $(-2)^3$ means the entire quantity (-2) is being cubed, not just the 2.

Absolute Value with Negative Exponents

$|(-2)^3| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|(-2)^3| =$

Step-by-step solution

First, calculate $(-2)^3$ .

The expression $(-2)^3$ means $-2 \times -2 \times -2$ .

Calculating this yields $-8$ .

Taking the absolute value of $-8$ gives $8$ , because the absolute value of a negative number is its positive counterpart.

Final Answer

$8$

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate the exponent first, then apply absolute value
Technique: $(-2)^3 = -2 \times -2 \times -2 = -8$
Check: Verify $|-8| = 8$ is positive ✓

Common Mistakes

Avoid these frequent errors

Taking absolute value before calculating the exponent
Don't find $|2^3| = 8$ first! This ignores the negative sign and gives wrong results. The expression means take (-2) cubed first, then find absolute value. Always calculate inside the absolute value bars first.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

$\left|18\right|=$

FAQ

Everything you need to know about this question

Why is $(-2)^3$ negative when we're multiplying negative numbers?

When you multiply an odd number of negative factors, the result is negative. Here we have three negative twos: $-2 \times -2 \times -2$ , so the answer is $-8$ .

What's the difference between $(-2)^3$ and $-2^3$ ?

$(-2)^3 = -8$ because the parentheses include the negative sign in the base. But $-2^3 = -(2^3) = -8$ means negative of 2 cubed. In this case, both equal -8, but they can differ with even exponents!

Does absolute value always make numbers positive?

Yes! The absolute value of any real number is always non-negative. $|8| = 8$ and $|-8| = 8$ . Think of it as the distance from zero on a number line.

How do I remember the order of operations with absolute value?

Use PEMDAS! Absolute value bars act like parentheses, so calculate everything inside them first. Only after you get the result inside do you apply the absolute value operation.

What if I calculated $2^3 = 8$ instead?

That's a common mistake! You must keep the negative sign as part of the base when it's in parentheses. $(-2)^3$ means the entire quantity (-2) is being cubed, not just the 2.

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Calculate the Absolute Value: Solving |-2 Cubed|

Absolute Value with Negative Exponents

❤️ Continue Your Math Journey!

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 $(-2)^3$ negative when we're multiplying negative numbers?

What's the difference between $(-2)^3$ and $-2^3$ ?

Does absolute value always make numbers positive?

How do I remember the order of operations with absolute value?

What if I calculated $2^3 = 8$ instead?

🌟 Unlock Your Math Potential

More Questions

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Evaluate the Absolute Value in Exponentiation: Solve |(-4)^2|

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Solve |9/3 - 4|: Absolute Value with Fractions

Evaluate the Absolute Value Expression: |4 - 3¹| Step-by-Step

Calculate the Absolute Value: Solving |-2 Cubed|

Absolute Value with Negative Exponents

❤️ Continue Your Math Journey!

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 (−2)3(-2)^3(−2)3 negative when we're multiplying negative numbers?

What's the difference between (−2)3(-2)^3(−2)3 and −23-2^3−23?

Does absolute value always make numbers positive?

How do I remember the order of operations with absolute value?

What if I calculated 23=82^3 = 823=8 instead?

🌟 Unlock Your Math Potential

More Questions

Absolute value

Evaluate the Absolute Value in Exponentiation: Solve |(-4)^2|

Evaluating Absolute Value of Negative One-Power Expression: |(-5)^1|

Solve |9/3 - 4|: Absolute Value with Fractions

Evaluate the Absolute Value Expression: |4 - 3¹| Step-by-Step

Why is $(-2)^3$ negative when we're multiplying negative numbers?

What's the difference between $(-2)^3$ and $-2^3$ ?

What if I calculated $2^3 = 8$ instead?