Calculate 6^5: Converting an Exponential Expression to an Integer

Q: What's the difference between 6 × 5 and 6⁵?

6 × 5 = 30 (simple multiplication), but $ 6^5 $ = 7776 (multiply 6 by itself 5 times). The small raised number is an exponent, not a multiplication sign!

Q: Is there a faster way than multiplying step by step?

You can break it down using exponent rules: $ 6^5 = 6^2 \times 6^3 = 36 \times 216 = 7776 $. But for beginners, step-by-step is safer to avoid mistakes.

Q: How can I remember what 6⁵ means?

Think of it as "6 to the 5th power" - you're powering up 6 by using it as a factor 5 times: $ 6 \times 6 \times 6 \times 6 \times 6 $.

Q: What if I make an arithmetic mistake in the middle?

Always double-check each step! Write down: 6² = 36, 6³ = 216, 6⁴ = 1296, 6⁵ = 7776. If any step seems wrong, recalculate from there.

Exponentiation with Integer Base

Write the following as an integer:

$6^5=$

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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

00:20 Let's use this formula in our exercise

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

00:45 Let's calculate the multiplications

01:04 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

Write the following as an integer:

$6^5=$

Step-by-step solution

To solve the problem of finding $6^5$ and expressing it as an integer, we need to carry out the multiplication of $6$ by itself five times. Here is the step-by-step calculation:

Step 1: Multiply $6 \times 6$ which equals $36$ .
Step 2: Multiply $36 \times 6$ which results in $216$ .
Step 3: Multiply $216 \times 6$ obtaining $1296$ .
Step 4: Multiply $1296 \times 6$ to get $7776$ .

By following these calculations, we find that $6^5 = 7776$ .

Thus, the integer representation of $6^5$ is $7776$ .

Final Answer

7776

Key Points to Remember

Essential concepts to master this topic

Rule: Exponent tells you how many times to multiply the base
Technique: Calculate step-by-step: 6² = 36, then 36 × 6 = 216
Check: Count multiplications: 6 × 6 × 6 × 6 × 6 = 7776 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying when calculating exponents
Don't calculate 6⁵ as 6 × 5 = 30! This confuses exponents with multiplication and gives completely wrong answers. Always multiply the base by itself the number of times shown in the exponent.

Practice Quiz

Test your knowledge with interactive questions

$$ 6^2= $$

FAQ

Everything you need to know about this question

What's the difference between 6 × 5 and 6⁵?

6 × 5 = 30 (simple multiplication), but $6^5$ = 7776 (multiply 6 by itself 5 times). The small raised number is an exponent, not a multiplication sign!

Is there a faster way than multiplying step by step?

You can break it down using exponent rules: $6^5 = 6^2 \times 6^3 = 36 \times 216 = 7776$ . But for beginners, step-by-step is safer to avoid mistakes.

How can I remember what 6⁵ means?

Think of it as "6 to the 5th power" - you're powering up 6 by using it as a factor 5 times: $6 \times 6 \times 6 \times 6 \times 6$ .

What if I make an arithmetic mistake in the middle?

Always double-check each step! Write down: 6² = 36, 6³ = 216, 6⁴ = 1296, 6⁵ = 7776. If any step seems wrong, recalculate from there.

Why is 6⁵ so much bigger than 6⁴?

Each time you increase the exponent by 1, you multiply by the base again! So $6^5 = 6^4 \times 6 = 1296 \times 6 = 7776$ . Exponential growth is very fast!

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