Math Problem Statement

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

[\dfrac{y^{5}}{y^3}=]

Solution

To simplify the expression y5y3\frac{y^5}{y^3}, you can use the quotient rule of exponents, which states:

aman=amn\frac{a^m}{a^n} = a^{m-n}

Applying this to your expression:

y5y3=y53=y2\frac{y^5}{y^3} = y^{5-3} = y^2

So, the simplified expression is:

y2y^2

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

Here are 5 related questions:

  1. How would you simplify y7y4\frac{y^7}{y^4}?
  2. What is the value of x5x2\frac{x^5}{x^2} when x=2x = 2?
  3. How do you simplify y6y6\frac{y^6}{y^6}?
  4. Can you apply the quotient rule to simplify 2y54y3\frac{2y^5}{4y^3}?
  5. What is the general rule for dividing powers with the same base?

Tip: Always subtract the exponent in the denominator from the exponent in the numerator when simplifying expressions of the same base.

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Math Problem Analysis

Mathematical Concepts

Exponents
Quotient Rule of Exponents

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8