Calculate 5³: Finding the Cube of Number 5

Q: What's the difference between 5³ and 5 × 3?

Big difference! $ 5^3 $ means 5 × 5 × 5 = 125, while 5 × 3 = 15. The exponent tells you how many times to use 5 as a factor, not what to multiply 5 by.

Q: How do I remember what cubed means?

Think of a cube shape! A cube has 3 dimensions (length × width × height), so when we 'cube' a number, we multiply it 3 times: $ 5^3 = 5 \times 5 \times 5 $.

Q: What if I got 25 as my answer?

You probably calculated $ 5^2 = 5 \times 5 = 25 $ instead of $ 5^3 $. Remember: the exponent 3 means you need three factors of 5, not just two!

Exponent Calculation with Perfect Cubes

Check the correct answer:

$5^3=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's use the power formula

00:06 Any number (X) to the power of (N)

00:09 equals X multiplied by itself N times

00:16 Let's use this formula in our exercise

00:28 Let's break down the power into multiplications

00:40 Let's calculate the multiplications

00:53 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

Check the correct answer:

$5^3=$

Step-by-step solution

To solve the problem of finding $5^3$ , we will proceed as follows:

Step 1: Identify that $5^3$ means $5$ raised to the power of 3, which is equivalent to multiplying 5 by itself 3 times.
Step 2: Compute the expression: $5^3 = 5 \times 5 \times 5$ .
Step 3: Perform the multiplication in two stages for clarity:

First, calculate $5 \times 5 = 25$ .
Next, take the result from the first calculation and multiply by 5 again: $25 \times 5 = 125$ .

Therefore, the value of $5^3$ is 125.

This matches with one of the provided choices, which is 125.

Final Answer

125

Key Points to Remember

Essential concepts to master this topic

Exponent Rule: $a^3$ means multiply the base by itself 3 times
Technique: Calculate step-by-step: $5^3 = 5 \times 5 \times 5 = 25 \times 5 = 125$
Check: Verify by counting factors: 5 appears exactly 3 times in the multiplication ✓

Common Mistakes

Avoid these frequent errors

Multiplying the base by the exponent
Don't calculate $5^3$ as 5 × 3 = 15! This confuses exponents with multiplication and gives completely wrong results. Always multiply the base by itself as many times as the exponent indicates.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

What's the difference between 5³ and 5 × 3?

Big difference! $5^3$ means 5 × 5 × 5 = 125, while 5 × 3 = 15. The exponent tells you how many times to use 5 as a factor, not what to multiply 5 by.

How do I remember what cubed means?

Think of a cube shape! A cube has 3 dimensions (length × width × height), so when we 'cube' a number, we multiply it 3 times: $5^3 = 5 \times 5 \times 5$ .

Can I use a calculator for this?

Sure! But it's great practice to do small cubes by hand. Try calculating $5 \times 5 = 25$ first, then $25 \times 5 = 125$ . This builds your number sense!

Why is 125 called a perfect cube?

Because 125 is the result of cubing a whole number (5). Perfect cubes are: 1, 8, 27, 64, 125, 216... They're the cubes of 1, 2, 3, 4, 5, 6...

What if I got 25 as my answer?

You probably calculated $5^2 = 5 \times 5 = 25$ instead of $5^3$ . Remember: the exponent 3 means you need three factors of 5, not just two!

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