Math Problem Statement

(4x^2y^-3)(2x^-3y^2)

Solution

To simplify the expression (4x2y3)(2x3y2)(4x^2y^{-3})(2x^{-3}y^2), follow these steps:

  1. Multiply the constants:
    4×2=84 \times 2 = 8

  2. Combine the xx terms:
    x2×x3=x2+(3)=x1x^2 \times x^{-3} = x^{2 + (-3)} = x^{-1}

  3. Combine the yy terms:
    y3×y2=y3+2=y1y^{-3} \times y^2 = y^{-3 + 2} = y^{-1}

Now, put everything together:

(4x2y3)(2x3y2)=8x1y1(4x^2y^{-3})(2x^{-3}y^2) = 8x^{-1}y^{-1}

Finally, express the negative exponents as fractions:

8x1y1=8xy8x^{-1}y^{-1} = \frac{8}{xy}

So, the simplified expression is 8xy\frac{8}{xy}.

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

Here are five related questions you might find useful:

  1. How would the expression change if one of the exponents was positive?
  2. What happens if you multiply two expressions with the same base but different exponents?
  3. How do you handle negative exponents in a fraction?
  4. How do you simplify an expression with both positive and negative exponents?
  5. Can you simplify (x4y2)(3x1y3)(x^4y^{-2})(3x^{-1}y^3)?

Tip: Always simplify exponents first before combining the terms when multiplying expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponent Rules
Multiplying Expressions

Formulas

Product of Powers Rule: a^m * a^n = a^(m+n)
Simplifying Negative Exponents: a^-n = 1/a^n

Theorems

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Suitable Grade Level

Grades 8-10