Math Problem Statement

0,2^-3

Solution

The expression you have provided is:

0,230,2^{-3}

This is equivalent to:

(210)3=(15)3=153=1125\left( \frac{2}{10} \right)^{-3} = \left( \frac{1}{5} \right)^{-3} = \frac{1}{5^3} = \frac{1}{125}

So, the result is:

11250.008\frac{1}{125} \approx 0.008

Would you like more details on this, or have any questions?

Here are 5 related questions to expand your understanding:

  1. How do negative exponents work in general?
  2. What is the difference between a positive and a negative exponent?
  3. How does fractional base handling differ in exponents?
  4. How do you simplify powers of fractions?
  5. What are some real-life applications of negative exponents?

Tip: Negative exponents indicate reciprocal values. For example, xn=1xnx^{-n} = \frac{1}{x^n}.

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Exponents
Fractions

Formulas

x^{-n} = \frac{1}{x^n}
a^{-n} = \frac{1}{a^n}
Fractional base handling: \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^n

Theorems

Law of Negative Exponents
Reciprocal Rule

Suitable Grade Level

Grades 7-8