Question

simplify ((3x^2y^{-5})^3).
a) (27x^6y^{15})
b) (27x^6y^{-15})
c) (9x^6y^{-15})
d) (27x^5y^2)

Explanation:

Step1: Apply power to coefficient

$3^3 = 27$

Step2: Apply power to $x$-term

$(x^2)^3 = x^{2\times3}=x^6$

Step3: Apply power to $y$-term

$(y^{-5})^3 = y^{-5\times3}=y^{-15}$

Step4: Combine all terms

$27 \times x^6 \times y^{-15} = 27x^{6}y^{-15}$

Answer:

B) $27x^{6}y^{-15}$