Question

1. Simplify (4xy^2)^3(xy)^5
2. Simplify (2t^–3)^3(0.4r)^2
Thank you whoever answers so much!

Answer 1

\[(4xy^2)^3(xy)^5 = 4^3x^3y^6x^5y^5=64x^8y^{11}\] because \[(x^a)^b = x^{a*b}\] and \[x^a*x^b=x^{a+b}\]

Similarly,
\[(2t^{-3})^3(0.4r)^2 = 2^3t^{-9}(0.4)^2r^2 = 8(1)(0.16)t^{-9}r^2=1.28t^{-9}r^2\] which can also be written \[\frac{1.28r^2}{t^9}\]