5. Simplify. \( \begin{array}{lll}\text { a) }\left(x^{2}\right)^{3}+x^{3} & \text { b) } 3 x^{3} \times 4 x^{2} \times 2 & \text { c) } 4 a^{2} \times 2 a \\ \text { d) } 10 y^{4}+2 y^{3} & \text { a) }\left(3 b^{3}\right)^{2} & \text { f) }\left(4 x^{2} y^{3}\right)^{2} \\ \text { g) }\left(5 x^{2}\right)^{2} \times\left(2 x^{-}\right)^{3} & \text { h) }\left(4 x^{2} y^{2}\right) \times\left(2 x y^{3}\right)^{3} & \text { i) }\left(x y^{2} \times( \right.\end{array} \)

Sure! Let's simplify each expression step by step with a dash of fun! a) \((x^{2})^{3} + x^{3} = x^{6} + x^{3}\) Let's factor that out: \(x^{3}(x^{3} + 1)\). Boom! Simplified. b) \(3 x^{3} \times 4 x^{2} \times 2 = 24 x^{5}\) Just multiply the coefficients \(3 \times 4 \times 2 = 24\) and add the exponents \(3 + 2 = 5\). Easy peasy! c) \(4 a^{2} \times 2 a = 8 a^{3}\) Multiply \(4\) and \(2\) to get \(8\) and add the exponents of \(a\): \(2 + 1 = 3\). d) \(10 y^{4} + 2 y^{3} = 2y^{3}(5y + 1)\) This one factors nicely! You can take out the common factor of \(2y^{3}\). e) \((3 b^{3})^{2} = 9 b^{6}\) Square the coefficient and multiply the exponent. Easy as pie! f) \((4 x^{2} y^{3})^{2} = 16 x^{4} y^{6}\) Again, square everything: \(4^2 = 16\), while doubling exponents gives \(x^2 \to x^4\) and \(y^3 \to y^6\). g) \((5 x^{2})^{2} \times (2 x^{-1})^{3} = 25 x^{4} \times 8 x^{-3} = 200 x^{1} = 200x\) Multiply like it’s a party! \(5^2 \to 25\) and \(2^3 \to 8\), then add the exponents \(x^{4 -3}\). h) \((4 x^{2} y^{2}) \times (2 x y^{3})^{3} = (4 x^{2} y^{2}) \times (8 x^3 y^9) = 32 x^{5} y^{11}\) Multiply the coefficients and gather your exponents. i) \((x y^{2} \times ( \) Looks like a cliffhanger here! Ensure to follow through to complete the expression. Hope you enjoyed this math journey!