Solve 10^(-5): Converting Negative Power to Decimal Form

Q: Why does a negative exponent make the number smaller instead of negative?

The negative sign in the exponent doesn't make the result negative - it means "take the reciprocal"! Think of it as flipping the fraction: $ 10^{-5} = \frac{1}{10^5} $, which gives a positive decimal.

Q: How do I remember which way the decimal point moves?

For negative exponents, the decimal moves left! $ 10^{-5} $ means move the decimal 5 places left from 1.0 to get 0.00001.

Q: Is there a pattern with powers of 10?

Yes! $ 10^{-1} = 0.1 $, $ 10^{-2} = 0.01 $, $ 10^{-3} = 0.001 $. The number of zeros after the decimal equals the exponent!

Q: What if the base isn't 10?

The same rule applies! $ 2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125 $. Any base with a negative exponent becomes 1 divided by that base raised to the positive exponent.

Q: Can I use a calculator for this?

Absolutely! But understanding the concept helps you catch calculator errors. Try $ 10^{-5} $ on your calculator - you should get 0.00001 or 1E-5 (scientific notation).

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 According to the power laws, a number(A) when raised to the power of(-N)

00:06 equals 1 divided by the number(A) raised to the power of(N)

00:09 Let's apply this to the question, the formula works from number to fraction and vice versa

00:12 We obtain 1 divided by (10) raised to the power of (5)

00:15 Let's proceed to solve 10 raised to the power of 5 according to the power laws

00:18 Which is in fact 10 multiplied by 10, 5 times

00:24 Insert this into the question

00:38 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$10^{-5}=?$

2

Step-by-step solution

First, let's recall the negative exponent rule:

$b^{-n}=\frac{1}{b^n}$ We'll apply it to the expression we received:

$10^{-5}=\frac{1}{10^5}=\frac{1}{100000}=0.00001$ In the final steps, we performed the exponentiation in the numerator and then wrote the answer as a decimal.

Therefore, the correct answer is option A.

3

Final Answer

$0.00001$

Key Points to Remember

Essential concepts to master this topic

Rule: $b^{-n} = \frac{1}{b^n}$ converts negative exponent to positive
Technique: $10^{-5} = \frac{1}{10^5} = \frac{1}{100000} = 0.00001$
Check: Count decimal places: 5 zeros after decimal point matches exponent 5 ✓

Common Mistakes

Avoid these frequent errors

Multiplying base by negative exponent
Don't calculate $10^{-5}$ as 10 × (-5) = -50! This completely ignores exponent rules and gives a negative number instead of a positive decimal. Always use the negative exponent rule: $10^{-5} = \frac{1}{10^5}$ .

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why does a negative exponent make the number smaller instead of negative?

+

The negative sign in the exponent doesn't make the result negative - it means "take the reciprocal"! Think of it as flipping the fraction: $10^{-5} = \frac{1}{10^5}$ , which gives a positive decimal.

How do I remember which way the decimal point moves?

+

For negative exponents, the decimal moves left! $10^{-5}$ means move the decimal 5 places left from 1.0 to get 0.00001.

Is there a pattern with powers of 10?

+

Yes! $10^{-1} = 0.1$ , $10^{-2} = 0.01$ , $10^{-3} = 0.001$ . The number of zeros after the decimal equals the exponent!

What if the base isn't 10?

+

The same rule applies! $2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125$ . Any base with a negative exponent becomes 1 divided by that base raised to the positive exponent.

Can I use a calculator for this?

+

Absolutely! But understanding the concept helps you catch calculator errors. Try $10^{-5}$ on your calculator - you should get 0.00001 or 1E-5 (scientific notation).

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Solve 10^(-5): Converting Negative Power to Decimal Form

Negative Exponents with Powers of Ten

❤️ 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

Why does a negative exponent make the number smaller instead of negative?

How do I remember which way the decimal point moves?

Is there a pattern with powers of 10?

What if the base isn't 10?

Can I use a calculator for this?

🌟 Unlock Your Math Potential

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