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

Problem

(2*x^4*y^(−3))^(−1)

Solution

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

(2)^(−1)*(x^4)^(−1)*(y^(−3))^(−1)

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

2^(−1)*x^(4⋅(−1))*y^(−3⋅(−1))

2^(−1)*x^(−4)*y^3

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

(y^3)/(2^1*x^4)

4. Simplify the numerical coefficient in the denominator.

(y^3)/(2*x^4)

Final Answer

(2*x^4*y^(−3))^(−1)=(y^3)/(2*x^4)

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