Simplify 2x^3y^-3*(2x^-1y^3)

Problem

2*x^3*y^(−3)⋅(2*x^(−1)*y^3)

Solution

1. Group the coefficients and variables by rearranging the terms using the commutative property of multiplication.

2⋅2⋅x^3⋅x^(−1)⋅y^(−3)⋅y^3

2. Multiply the numerical coefficients together.

4⋅x^3⋅x^(−1)⋅y^(−3)⋅y^3

3. Apply the product rule for exponents a^m⋅a^n=a^(m+n) to the x variables by adding their exponents.

4⋅x^(3+(−1))⋅y^(−3)⋅y^3

4*x^2⋅y^(−3)⋅y^3

4. Apply the product rule for exponents to the y variables by adding their exponents.

4*x^2⋅y^(−3+3)

4*x^2⋅y^0

5. Simplify the zero exponent using the rule y^0=1 for y≠0

4*x^2⋅1

4*x^2

Final Answer

2*x^3*y^(−3)⋅(2*x^(−1)*y^3)=4*x^2

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