Evaluate (-5)³ + 5²: Combining Cube and Square Powers

Q: Why does $ (-5)^3 $ equal -125 but $ 5^2 $ equals +25?

The exponent determines the sign! With odd exponents, negative bases stay negative. With even exponents, any base becomes positive because you multiply pairs of negatives.

Q: How do I remember the sign rules for exponents?

Think of it as multiplication patterns: $ (-) \times (-) = (+) $. So even exponents always give positive results, while odd exponents keep the original sign.

Q: What's the difference between $ (-5)^2 $ and $ -5^2 $ ?

$ (-5)^2 = 25 $ because parentheses include the negative in the base. But $ -5^2 = -25 $ means negative of five squared!

Q: Do I add the exponents when I see different powers?

No! You only add exponents when multiplying the same base. Here we have $ (-5)^3 + 5^2 $, so calculate each power separately, then add the results.

Q: How can I check if my final answer is correct?

Work backwards: $ -125 + 25 = -100 $. You can also use a calculator to verify $ (-5)^3 = -125 $ and $ 5^2 = 25 $ separately!

Exponent Rules with Negative Base Powers

$(-5)^3+5^2=$

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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

00:07 Odd power, therefore the sign remains negative

00:14 Let's calculate the powers

00:22 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

$(-5)^3+5^2=$

Step-by-step solution

To solve this problem, we'll calculate each part of the expression separately:

Step 1: Calculate $(-5)^3$ . Since $3$ is odd, $(-5)^3 = (-5) \cdot (-5) \cdot (-5) = -125$ .
Step 2: Calculate $5^2$ . As $2$ is an even number, $5^2 = 5 \cdot 5 = 25$ .
Step 3: Add the results of the two calculations: $-125 + 25$ .

Now, let's work through each step:
Step 1: We calculated that $(-5)^3 = -125$ .
Step 2: We found that $5^2 = 25$ .
Step 3: Adding these results: $-125 + 25 = -100$ .

Therefore, the solution to the problem is $-100$ .

Final Answer

$-100$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative base with odd exponent stays negative
Technique: Calculate $(-5)^3 = (-5) \cdot (-5) \cdot (-5) = -125$
Check: Verify signs: negative cubed = negative, positive squared = positive ✓

Common Mistakes

Avoid these frequent errors

Ignoring the negative sign with odd exponents
Don't calculate $(-5)^3$ as $5^3 = 125$ = wrong positive result! Odd exponents preserve the negative sign, while even exponents make it positive. Always track the sign carefully through each multiplication.

Practice Quiz

Test your knowledge with interactive questions

$$ (-2)^7= $$

FAQ

Everything you need to know about this question

Why does $(-5)^3$ equal -125 but $5^2$ equals +25?

The exponent determines the sign! With odd exponents, negative bases stay negative. With even exponents, any base becomes positive because you multiply pairs of negatives.

How do I remember the sign rules for exponents?

Think of it as multiplication patterns: $(-) \times (-) = (+)$ . So even exponents always give positive results, while odd exponents keep the original sign.

What's the difference between $(-5)^2$ and $-5^2$ ?

$(-5)^2 = 25$ because parentheses include the negative in the base. But $-5^2 = -25$ means negative of five squared!

Do I add the exponents when I see different powers?

No! You only add exponents when multiplying the same base. Here we have $(-5)^3 + 5^2$ , so calculate each power separately, then add the results.

How can I check if my final answer is correct?

Work backwards: $-125 + 25 = -100$ . You can also use a calculator to verify $(-5)^3 = -125$ and $5^2 = 25$ separately!

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Evaluate (-5)³ + 5²: Combining Cube and Square Powers

Exponent Rules with Negative Base Powers

❤️ 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 $(-5)^3$ equal -125 but $5^2$ equals +25?

How do I remember the sign rules for exponents?

What's the difference between $(-5)^2$ and $-5^2$ ?

Do I add the exponents when I see different powers?

How can I check if my final answer is correct?

🌟 Unlock Your Math Potential

More Questions

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

Calculate 6² - (-6)²: Comparing Positive and Negative Squares

Solve (-(-2)²)² - 2³: Multiple Exponents and Negative Numbers

Evaluate -(-1)^100 × 2²: Step-by-Step Solution Guide

Evaluate (-5)³ + 5²: Combining Cube and Square Powers

Exponent Rules with Negative Base Powers

❤️ 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 (−5)3 (-5)^3 (−5)3 equal -125 but 52 5^2 52 equals +25?

How do I remember the sign rules for exponents?

What's the difference between (−5)2 (-5)^2 (−5)2 and −52 -5^2 −52?

Do I add the exponents when I see different powers?

How can I check if my final answer is correct?

🌟 Unlock Your Math Potential

More Questions

Powers of Negative Numbers

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

Calculate 6² - (-6)²: Comparing Positive and Negative Squares

Solve (-(-2)²)² - 2³: Multiple Exponents and Negative Numbers

Evaluate -(-1)^100 × 2²: Step-by-Step Solution Guide

Why does $(-5)^3$ equal -125 but $5^2$ equals +25?

What's the difference between $(-5)^2$ and $-5^2$ ?