Simplify ((xy^-2z^-3)/(x^2y^3z^-4))^-3

Problem

((x*y(−2)*z(−3))/(x2*y3*z(−4)))(−3)

Solution

1. Simplify the expression inside the parentheses by applying the quotient rule for exponents, am/an=a(m−n) for each variable.

(x1)/(x2)=x(1−2)=x(−1)

(y(−2))/(y3)=y(−2−3)=y(−5)

(z(−3))/(z(−4))=z(−3−(−4))=z1

2. Rewrite the inner expression using the simplified variables.

(x(−1)*y(−5)*z1)(−3)

3. Apply the power of a power rule, (am)n=a(m⋅n) by multiplying each exponent inside the parentheses by −3

x(−1⋅−3)=x3

y(−5⋅−3)=y15

z(1⋅−3)=z(−3)

4. Express with positive exponents by moving the variable with the negative exponent to the denominator.

x3*y15*z(−3)=(x3*y15)/(z3)

Final Answer

((x*y(−2)*z(−3))/(x2*y3*z(−4)))(−3)=(x3*y15)/(z3)

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