Math Problem Statement

Simplify the following using exponent laws. Write the answer with positive exponents in rational form

Simplify the following using exponent laws. Write the answer with positive exponents in rational form: (x^(-5) * x^3) / x^(-2)

Solution

sympy import symbols, simplify

Define the variable

x = symbols('x')

Define the expression

expression = (x**-5 * x3) / x-2

Simplify the expression

simplified_expression = simplify(expression)

simplified_expressionThe given expression simplifies to 1 using the laws of exponents.

Would you like a detailed step-by-step explanation or assistance with related questions?

Here are 5 related questions to expand understanding:

  1. How do the laws of exponents work for multiplication and division?
  2. Can you explain the importance of rewriting expressions with positive exponents?
  3. What is the difference between rationalizing exponents and simplifying expressions?
  4. How would the solution change if the base of the exponents was different?
  5. Can negative exponents ever result in negative values in expressions?

Tip: Always combine and simplify like terms step-by-step to avoid errors in calculations.

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Math Problem Analysis

Mathematical Concepts

Laws of Exponents
Simplifying Expressions

Formulas

Product of Powers: x^a * x^b = x^(a+b)
Quotient of Powers: x^a / x^b = x^(a-b)

Theorems

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Suitable Grade Level

Grades 8-10

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