Calculate 13^4: Converting Power to Integer Form

Q: Is there a shortcut to calculate $ 13^4 $ without doing all the multiplication?

The step-by-step method shown is actually the most reliable shortcut! First find $ 13^2 = 169 $, then $ (13^2)^2 = 169^2 = 28561 $. This uses smaller, manageable multiplications.

Q: Why can't I just use a calculator?

While calculators are great tools, understanding the process helps you catch errors and builds number sense. Plus, showing your work step-by-step demonstrates mathematical reasoning!

Q: How do I avoid making arithmetic mistakes in the multiplication?

Break it down: Use the distributive property like $ 169 \times 13 = 169 \times (10 + 3) = 1690 + 507 $. This makes large multiplications more manageable and reduces errors.

Q: Are there patterns I can use for powers of 13?

Yes! Notice that $ 13^2 = 169 $ ends in 9, $ 13^3 = 2197 $ ends in 7, and $ 13^4 = 28561 $ ends in 1. Last digit patterns can help you check if your answer is reasonable.

Q: Is 28561 really the only correct answer?

Absolutely! Exponentiation gives exactly one result. You can verify: $ 13 \times 13 \times 13 \times 13 = 28561 $. Any other answer means there was a calculation error somewhere.

Exponent Calculation with Step-by-Step Multiplication

Write the following as an integer:

$13^4=$

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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

00:17 Let's use this formula in our exercise

00:21 Let's break down the power into multiplications

00:38 Let's calculate the multiplications

00:46 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:

$13^4=$

Step-by-step solution

To solve this problem, we will perform step-by-step calculations to find $13^4$ :

Step 1: Calculate $13^2$ . We have $13 \times 13 = 169$ .
Step 2: Calculate $13^3$ using the result from Step 1. We multiply $169 \times 13$ . Performing the multiplication:
$169 \times 13 = 169 \times (10 + 3) = 169 \times 10 + 169 \times 3 = 1690 + 507 = 2197$ .
Step 3: Calculate $13^4$ using the result from Step 2. Multiply $2197 \times 13$ . Performing the multiplication:
$2197 \times 13 = 2197 \times (10 + 3) = 2197 \times 10 + 2197 \times 3 = 21970 + 6591 = 28561$ .

Therefore, the value of $13^4$ is 28561, which corresponds to choice (2).

Final Answer

28561

Key Points to Remember

Essential concepts to master this topic

Exponent Rule: $a^n = a \times a \times ... \times a$ (n times)
Building Technique: Calculate $13^2 = 169$ , then $13^3 = 169 \times 13 = 2197$
Verification: Work backwards: does $\sqrt[4]{28561} = 13$ ? Check: $13 \times 13 \times 13 \times 13 = 28561$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying exponent by base instead of repeated multiplication
Don't calculate $13^4 = 13 \times 4 = 52$ ! This confuses multiplication with exponentiation and gives a completely wrong result. Always remember that $13^4$ means thirteen multiplied by itself four times: $13 \times 13 \times 13 \times 13$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Is there a shortcut to calculate $13^4$ without doing all the multiplication?

The step-by-step method shown is actually the most reliable shortcut! First find $13^2 = 169$ , then $(13^2)^2 = 169^2 = 28561$ . This uses smaller, manageable multiplications.

Why can't I just use a calculator?

While calculators are great tools, understanding the process helps you catch errors and builds number sense. Plus, showing your work step-by-step demonstrates mathematical reasoning!

How do I avoid making arithmetic mistakes in the multiplication?

Break it down: Use the distributive property like $169 \times 13 = 169 \times (10 + 3) = 1690 + 507$ . This makes large multiplications more manageable and reduces errors.

What if I get a different answer than the choices given?

Double-check each multiplication step carefully! Common errors happen when multiplying by 13. Try using different methods like the distributive property or column multiplication to verify your work.

Are there patterns I can use for powers of 13?

Yes! Notice that $13^2 = 169$ ends in 9, $13^3 = 2197$ ends in 7, and $13^4 = 28561$ ends in 1. Last digit patterns can help you check if your answer is reasonable.

Is 28561 really the only correct answer?

Absolutely! Exponentiation gives exactly one result. You can verify: $13 \times 13 \times 13 \times 13 = 28561$ . Any other answer means there was a calculation error somewhere.

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Calculate 13^4: Converting Power to Integer Form

Exponent Calculation with Step-by-Step Multiplication

❤️ 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

Is there a shortcut to calculate $13^4$ without doing all the multiplication?

Why can't I just use a calculator?

How do I avoid making arithmetic mistakes in the multiplication?

What if I get a different answer than the choices given?

Are there patterns I can use for powers of 13?

Is 28561 really the only correct answer?

🌟 Unlock Your Math Potential

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Calculate 13^4: Converting Power to Integer Form

Exponent Calculation with Step-by-Step Multiplication

❤️ 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

Is there a shortcut to calculate 134 13^4 134 without doing all the multiplication?

Why can't I just use a calculator?

How do I avoid making arithmetic mistakes in the multiplication?

What if I get a different answer than the choices given?

Are there patterns I can use for powers of 13?

Is 28561 really the only correct answer?

🌟 Unlock Your Math Potential

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Is there a shortcut to calculate $13^4$ without doing all the multiplication?