Questions: (27 x^(-6) y^9 / z^9)^(1 / 3) =
A. y^3 / (x^2 z^3)
B. 3 y^3 x^2 z^3
C. 3 x^3 / (y^2 z^3)
D. y^3 / (3 x^2 z^3)
E. 3 y^3 / (x^2 z^3)
Transcript text: $\left(\frac{27 x^{-6} y^{9}}{z^{9}}\right)^{1 / 3}=$
A. $\frac{y^{3}}{x^{2} z^{3}}$
B. $3 y^{3} x^{2} z^{3}$
C. $\frac{3 x^{3}}{y^{2} z^{3}}$
D. $\frac{y^{3}}{3 x^{2} z^{3}}$
E. $\frac{3 y^{3}}{x^{2} z^{3}}$
Solution
Solution Steps
Step 1: Simplify the expression inside the parentheses
The given expression is:
(z927x−6y9)1/3
First, recognize that 27 is a perfect cube, since 27=33. Rewrite the expression as:
(z933x−6y9)1/3
Step 2: Apply the exponent 1/3 to each term
Using the property (am)n=am⋅n, apply the exponent 1/3 to each term inside the parentheses:
33⋅31⋅x−6⋅31⋅y9⋅31⋅z−9⋅31
Simplify the exponents:
31⋅x−2⋅y3⋅z−3
This simplifies to:
3⋅x−2⋅y3⋅z−3
Step 3: Rewrite the expression with positive exponents
To make the expression more readable, rewrite x−2 and z−3 as x21 and z31, respectively:
3⋅x21⋅y3⋅z31
Combine the terms:
x2z33y3
Final Answer
The simplified form of the expression is:
x2z33y3
The correct choice is E.