Math Problem Statement

10^-5

Solution

The expression 10510^{-5} means "10 raised to the power of -5." A negative exponent represents the reciprocal of the base raised to the corresponding positive exponent.

So, 10510^{-5} can be rewritten as:

105=1105=1100000=0.0000110^{-5} = \frac{1}{10^5} = \frac{1}{100000} = 0.00001

Thus, 105=0.0000110^{-5} = 0.00001.

Would you like further explanation or any details on this? Here are 5 related questions to explore this topic further:

  1. What is the value of 10610^{-6}?
  2. How do you multiply numbers with exponents, like 103×10210^3 \times 10^{-2}?
  3. How does the exponent rule apply to fractions like (12)3\left( \frac{1}{2} \right)^{-3}?
  4. What happens when a number with a negative exponent is squared, such as (105)2(10^{-5})^2?
  5. Can you explain the difference between positive and negative exponents?

Tip: Negative exponents flip the base to the reciprocal and apply the positive exponent.

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Math Problem Analysis

Mathematical Concepts

Exponents
Powers of 10
Negative Exponents

Formulas

a^(-n) = 1/a^n
10^(-5) = 1/10^5 = 0.00001

Theorems

Negative exponent rule: a^(-n) = 1/a^n

Suitable Grade Level

Grades 5-7