Math Problem Statement

What is the simplified form of 1/a^7?

Solution

The expression in the image is:

1a7\frac{1}{a^7}

This can be rewritten using the properties of exponents as:

a7a^{-7}

Thus, 1a7=a7\frac{1}{a^7} = a^{-7}.

Would you like further details or have any questions on this?

Here are five related questions to explore further:

  1. How do you simplify expressions with negative exponents?
  2. What is the rule for multiplying terms with the same base but different exponents?
  3. How would you solve 1an\frac{1}{a^n} for any value of nn?
  4. What happens when you multiply two terms with negative exponents?
  5. How do you handle fractional exponents?

Tip: A negative exponent represents the reciprocal of the base raised to the positive exponent. For example, an=1ana^{-n} = \frac{1}{a^n}.

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Exponents
Reciprocal

Formulas

1/a^n = a^(-n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 8-10