Evaluate the Expression: Finding the Value of 10,000¹

Q: Why does any number to the power of 1 just equal itself?

Think of exponents as repeated multiplication. When you have $ 10,000^1 $, you're multiplying 10,000 by itself one time, which just gives you 10,000!

Q: How is this different from 10,000 squared?

$ 10,000^2 $ means $ 10,000 \times 10,000 = 100,000,000 $, while $ 10,000^1 = 10,000 $. The exponent tells you how many times to use the base as a factor.

Q: Is 10,000 × 1 really the same as 10,000¹?

Yes! Both equal 10,000. The expression $ 10,000 \times 1 $ uses the identity property of multiplication (anything times 1 equals itself), just like $ 10,000^1 $ uses the identity property of exponents.

Q: Do negative numbers follow the same rule?

Absolutely! Whether positive or negative, any number to the first power equals itself. For example: $ (-5)^1 = -5 $ and $ (0.25)^1 = 0.25 $.

Q: What about zero to the first power?

$ 0^1 = 0 $! Zero follows the same rule. The only tricky case is $ 0^0 $, which is undefined, but that's a different topic entirely.

Exponent Rules with Power of One

Which of the following is equivalent to the expression below?

$10,000^1$

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Step-by-step video solution

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00:05 Let's solve this problem step-by-step.

00:09 If you raise any number, let's call it A, to the power of One, the answer is just the number A itself.

00:17 And that's how we find the solution to the question! Great job!

Step-by-step written solution

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Understand the problem

Which of the following is equivalent to the expression below?

$10,000^1$

Step-by-step solution

To solve this problem, we will apply the rule of exponents:

Any number raised to the power of 1 remains unchanged. Therefore, by the identity property of exponents, $10,000^1 = 10,000$ .

Given the choices:

$10,000 \cdot 10,000$ : This is $10,000^2$ .
$10,000 \cdot 1$ : Simplifying this expression yields 10,000, which is equivalent to $10,000^1$ .
$10,000 + 10,000$ : This results in 20,000, not equivalent to $10,000^1$ .
$10,000 - 10,000$ : This results in 0, not equivalent to $10,000^1$ .

Therefore, the correct choice is $10,000 \cdot 1$ , which simplifies to 10,000, making it equivalent to $10,000^1$ .

Thus, the expression $10,000^1$ is equivalent to:

$10,000 \cdot 1$

Final Answer

$10,000\cdot1$

Key Points to Remember

Essential concepts to master this topic

Identity Rule: Any number raised to power 1 equals itself
Technique: $10,000^1 = 10,000 \times 1 = 10,000$
Check: Verify answer equals original base number: $10,000^1 = 10,000$ ✓

Common Mistakes

Avoid these frequent errors

Confusing exponent 1 with multiplication or squaring
Don't think $10,000^1$ means $10,000 \times 10,000$ = 100,000,000! That would be $10,000^2$ . The exponent 1 means the number stays exactly the same. Always remember: any number to the first power equals itself.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Why does any number to the power of 1 just equal itself?

Think of exponents as repeated multiplication. When you have $10,000^1$ , you're multiplying 10,000 by itself one time, which just gives you 10,000!

How is this different from 10,000 squared?

$10,000^2$ means $10,000 \times 10,000 = 100,000,000$ , while $10,000^1 = 10,000$ . The exponent tells you how many times to use the base as a factor.

Is 10,000 × 1 really the same as 10,000¹?

Yes! Both equal 10,000. The expression $10,000 \times 1$ uses the identity property of multiplication (anything times 1 equals itself), just like $10,000^1$ uses the identity property of exponents.

Do negative numbers follow the same rule?

Absolutely! Whether positive or negative, any number to the first power equals itself. For example: $(-5)^1 = -5$ and $(0.25)^1 = 0.25$ .

What about zero to the first power?

$0^1 = 0$ ! Zero follows the same rule. The only tricky case is $0^0$ , which is undefined, but that's a different topic entirely.

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