Math Problem Statement

8(5)^-10

Solution

The expression you provided is:

8×(5)108 \times (5)^{-10}

To simplify this:

  1. The term 5105^{-10} is the same as 1510\frac{1}{5^{10}}.
  2. So the expression becomes:

8×1510=85108 \times \frac{1}{5^{10}} = \frac{8}{5^{10}}

  1. Now calculate 5105^{10}:

510=9,765,6255^{10} = 9,765,625

  1. Therefore, the simplified expression is:

89,765,625\frac{8}{9,765,625}

This is the most simplified form of the expression. Numerically, this fraction is approximately:

8÷9,765,6258.192×1078 \div 9,765,625 \approx 8.192 \times 10^{-7}

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:

  1. What is the meaning of a negative exponent?
  2. How would you simplify (2)5(2)^-5?
  3. Can you explain the difference between a positive and negative exponent?
  4. What is the value of 10310^{-3}?
  5. How do we handle fractional exponents?

Tip: Negative exponents indicate reciprocals; an=1ana^{-n} = \frac{1}{a^n}.

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Exponents
Simplification of Expressions

Formulas

a^{-n} = \frac{1}{a^n}
Multiplication of terms with exponents

Theorems

Laws of Exponents

Suitable Grade Level

Grades 8-10