Math Problem Statement

Rewrite the expression in the form [y^n].

[\dfrac{y^{-7}}{y^{-13}}=]

Solution

To rewrite the given expression in the form yny^n, follow the properties of exponents. Specifically, when dividing powers of the same base, subtract the exponents:

y7y13=y7(13)=y7+13=y6.\frac{y^{-7}}{y^{-13}} = y^{-7 - (-13)} = y^{-7 + 13} = y^6.

So, the expression simplifies to:

y6y^6

Would you like a detailed explanation or have any other questions?

Here are 5 related questions to consider:

  1. How do you simplify expressions with negative exponents?
  2. What is the rule for multiplying exponents with the same base?
  3. How do you simplify expressions with fractional exponents?
  4. How do you handle exponents when raising a power to a power?
  5. How do you simplify expressions involving exponents with different bases?

Tip: When dividing powers with the same base, always subtract the exponent in the denominator from the exponent in the numerator.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponentiation
Properties of Exponents

Formulas

Division of exponents: \(\frac{a^m}{a^n} = a^{m-n}\)

Theorems

Exponent rules for division

Suitable Grade Level

Grades 8-10