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

Problem

2*x3*y(−3)⋅(2*x(−1)*y3)

Solution

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

2⋅2⋅x3⋅x(−1)⋅y(−3)⋅y3

2. Multiply the numerical coefficients together.

4⋅x3⋅x(−1)⋅y(−3)⋅y3

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

4⋅x(3+(−1))⋅y(−3)⋅y3

4*x2⋅y(−3)⋅y3

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

4*x2⋅y(−3+3)

4*x2⋅y0

5. Simplify the zero exponent using the rule y0=1 for y≠0

4*x2⋅1

4*x2

Final Answer

2*x3*y(−3)⋅(2*x(−1)*y3)=4*x2

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