Math Problem Statement

Simplify: \( \frac{y^2}{y^{-3}} \)

Solution

Let's simplify the expression provided in the image:

y2y3\frac{y^2}{y^{-3}}

Step-by-step Solution:

  1. Apply the law of exponents: When dividing powers with the same base, subtract the exponents.

y2y3=y2(3)=y2+3=y5\frac{y^2}{y^{-3}} = y^{2 - (-3)} = y^{2 + 3} = y^5

Thus, the simplified expression is:

y5y^5

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

Here are some related questions you might explore:

  1. How do you simplify x3x2\frac{x^3}{x^{-2}}?
  2. What is the result of y2y3\frac{y^{-2}}{y^3}?
  3. How do the rules of exponents apply when multiplying powers?
  4. What happens when you raise a power to another power, e.g., (y2)3(y^2)^3?
  5. How do negative exponents relate to fractions?

Tip: Always remember that a negative exponent means you take the reciprocal of the base. For example, y3=1y3y^{-3} = \frac{1}{y^3}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Laws of Exponents

Formulas

\( \frac{a^m}{a^n} = a^{m-n} \)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 8-10