Solve the Basic Equation: Finding the Value Equal to -25

Q: Why does $(-5)^2$ equal 25 instead of -25?

Because the parentheses include the negative sign! So you're calculating $(-5) \times (-5) = 25$. The negative is part of the base being squared.

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

They're actually the same! Both equal -25. In $-(-5)^2$, you first square -5 to get 25, then apply the outer negative. In $-(5)^2$, you square 5 to get 25, then apply the negative.

Q: How do I remember when to use parentheses with negatives?

Think about what you want to happen: If you want to square the negative number itself, use $(-5)^2$. If you want the negative of a squared positive number, use $-(5)^2$.

Q: Should I calculate each option separately?

Yes! Work through each expression step by step using the order of operations. This helps you see exactly which ones give -25 and which ones don't.

Order of Operations with Exponents and Negatives

$-25=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Break down to exponent

00:03 Let's break down the exponent into multiplication, including the sign

00:07 It seems this option is not suitable

00:11 This option is exactly like the previous one just multiplied by minus

00:14 This option is suitable

00:19 Let's break down the exponent into multiplication, excluding the sign

00:24 This option is suitable

00:27 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

$-25=$

Step-by-step solution

To solve this problem, we'll evaluate each expression step by step:

Option a: $(-5)^2$
This implies that we first compute $(-5) \times (-5)$ which equals $25$ .
Option b: $-(-5)^2$
First, find $( -5)^2 = 25$ . Then, apply the negative sign, resulting in $-25$ .
Option c: $-(5)^2$
First, find $(5)^2 = 25$ . Then, apply the negative sign, resulting in $-25$ .

Options b and c both evaluate to $-25$ . Therefore, the correct answer is option d: "Answers b and c".

Final Answer

Answers b and c

Key Points to Remember

Essential concepts to master this topic

Rule: Parentheses determine whether negative applies to base or result
Technique: $(-5)^2 = 25$ but $-(5)^2 = -25$
Check: Substitute values step by step to verify each expression equals -25 ✓

Common Mistakes

Avoid these frequent errors

Confusing parentheses placement with negative signs
Don't treat $(-5)^2$ and $-(5)^2$ as the same = completely different answers! The first gives 25, the second gives -25. Always check if the negative is inside or outside the parentheses.

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 $(-5)^2$ equal 25 instead of -25?

Because the parentheses include the negative sign! So you're calculating $(-5) \times (-5) = 25$ . The negative is part of the base being squared.

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

They're actually the same! Both equal -25. In $-(-5)^2$ , you first square -5 to get 25, then apply the outer negative. In $-(5)^2$ , you square 5 to get 25, then apply the negative.

How do I remember when to use parentheses with negatives?

Think about what you want to happen: If you want to square the negative number itself, use $(-5)^2$ . If you want the negative of a squared positive number, use $-(5)^2$ .

Can multiple expressions equal the same value?

Absolutely! Different mathematical expressions can have the same value. That's why this problem asks which expressions equal -25, and the answer is both b and c.

Should I calculate each option separately?

Yes! Work through each expression step by step using the order of operations. This helps you see exactly which ones give -25 and which ones don't.

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Solve the Basic Equation: Finding the Value Equal to -25

Order of Operations with Exponents and Negatives

❤️ 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 $(-5)^2$ equal 25 instead of -25?

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

How do I remember when to use parentheses with negatives?

Can multiple expressions equal the same value?

Should I calculate each option separately?

🌟 Unlock Your Math Potential

More Questions

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Solve the Basic Equation: Finding the Value Equal to -25

Order of Operations with Exponents and Negatives

❤️ 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)2(-5)^2(−5)2 equal 25 instead of -25?

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

How do I remember when to use parentheses with negatives?

Can multiple expressions equal the same value?

Should I calculate each option separately?

🌟 Unlock Your Math Potential

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Why does $(-5)^2$ equal 25 instead of -25?

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