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

10−5=? 10^{-5}=?

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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

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1

Understand the problem

10−5=? 10^{-5}=?

2

Step-by-step solution

First, let's recall the negative exponent rule:

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

10−5=1105=1100000=0.00001 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 0.00001

Practice Quiz

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\( 112^0=\text{?} \)

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