Simplify ((xy^-2z^-3)/(2x^-2yz^2))^-3

Problem

((x*y(−2)*z(−3))/(2*x(−2)*y*z2))(−3)

Solution

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

(x(1−(−2))*y(−2−1)*z(−3−2))/2

(x3*y(−3)*z(−5))/2

2. Apply the negative exponent outside the parentheses by taking the reciprocal of the fraction and changing the exponent to positive.

(2/(x3*y(−3)*z(−5)))3

3. Distribute the exponent of 3 to every term inside the parentheses using the power of a power rule, (am)n=a(m*n)

2/((x3)3*(y(−3))3*(z(−5))3)

8/(x9*y(−9)*z(−15))

4. Eliminate negative exponents in the denominator by moving those terms to the numerator.

8*x(−9)*y9*z15

5. Move the remaining negative exponent to the denominator to ensure all exponents are positive.

(8*y9*z15)/(x9)

Final Answer

((x*y(−2)*z(−3))/(2*x(−2)*y*z2))(−3)=(8*y9*z15)/(x9)

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