Simplify (2x^4y^-3)^-1

Problem

(2*x4*y(−3))(−1)

Solution

1. Apply the power of a product rule, which states that (a*b*c)n=an*bn*cn Distribute the outer exponent −1 to each factor inside the parentheses.

(2)(−1)*(x4)(−1)*(y(−3))(−1)

2. Apply the power of a power rule, which states that (am)n=a(m⋅n) Multiply the exponents for each variable.

2(−1)*x(4⋅(−1))*y(−3⋅(−1))

2(−1)*x(−4)*y3

3. Apply the negative exponent rule, which states that a(−n)=1/(an) Move the terms with negative exponents to the denominator to make them positive.

(y3)/(2*x4)

4. Simplify the numerical coefficient in the denominator.

(y3)/(2*x4)

Final Answer

(2*x4*y(−3))(−1)=(y3)/(2*x4)

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