Solve the Cube Expression: Calculate 1³

Q: Why is 1 to any power always 1?

Because multiplying 1 by itself any number of times always gives 1! Think of it this way: 1×1 = 1, and 1×1×1 = 1, and so on. The number 1 is special in multiplication.

Q: What's the difference between 1³ and 1×3?

Exponents mean repeated multiplication, while regular multiplication is just once. So $ 1^3 = 1 \times 1 \times 1 = 1 $, but $ 1 \times 3 = 3 $. Very different operations!

Q: What if the exponent was 0 instead of 3?

Great question! $ 1^0 = 1 $ because any number (except 0) raised to the power of 0 equals 1. This is a special rule in mathematics.

Q: How do I remember this pattern?

Think of 1 as the "do nothing" number in multiplication. No matter how many times you multiply by 1, you get the same result. It's like adding zero - it doesn't change anything!

Exponentiation with Base One

Solve the following problem:

$1^3=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Break down from exponent to products

00:13 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

Solve the following problem:

$1^3=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate exponent rule
Step 3: Perform the calculation

Now, let's work through each step:
Step 1: The problem gives us the expression $1^3$ . This means we have a base of 1 and an exponent of 3.
Step 2: We'll use the exponentiation rule, which states that $a^n = a \times a \times \ldots \times a$ (n times).
Step 3: Since our base is 1, raising 1 to any power will still result in 1. Therefore, we can express this as $1 \times 1 \times 1 = 1$ .

Therefore, the solution to $1^3$ is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: Any base raised to any power follows $a^n = a \times a \times ... \times a$
Technique: $1^3 = 1 \times 1 \times 1 = 1$ since 1 multiplied gives 1
Check: Verify that 1 appears exactly 3 times in multiplication: 1×1×1 = 1 ✓

Common Mistakes

Avoid these frequent errors

Multiplying the base by the exponent
Don't calculate 1 × 3 = 3! This confuses multiplication with exponentiation and gives the wrong answer. Exponents mean repeated multiplication, not simple multiplication. Always multiply the base by itself the number of times shown in the exponent.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why is 1 to any power always 1?

Because multiplying 1 by itself any number of times always gives 1! Think of it this way: 1×1 = 1, and 1×1×1 = 1, and so on. The number 1 is special in multiplication.

What's the difference between 1³ and 1×3?

Exponents mean repeated multiplication, while regular multiplication is just once. So $1^3 = 1 \times 1 \times 1 = 1$ , but $1 \times 3 = 3$ . Very different operations!

Is this the same for other numbers?

No! Only the number 1 stays the same when raised to any power. Try $2^3 = 2 \times 2 \times 2 = 8$ or $3^3 = 3 \times 3 \times 3 = 27$ . They get much bigger!

What if the exponent was 0 instead of 3?

Great question! $1^0 = 1$ because any number (except 0) raised to the power of 0 equals 1. This is a special rule in mathematics.

How do I remember this pattern?

Think of 1 as the "do nothing" number in multiplication. No matter how many times you multiply by 1, you get the same result. It's like adding zero - it doesn't change anything!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Exponents Rules questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime