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

Simplify the expression by following steps: - step0: Solution: \(10y^{4}+2y^{3}\) Calculate or simplify the expression \( (x*y^2)*(x*y^2) \). Simplify the expression by following steps: - step0: Solution: \(xy^{2}xy^{2}\) - step1: Multiply the terms: \(x^{2}y^{2}\times y^{2}\) - step2: Multiply the terms: \(x^{2}y^{4}\) Calculate or simplify the expression \( 3*x^3*4*x^2*2 \). Simplify the expression by following steps: - step0: Solution: \(3x^{3}\times 4x^{2}\times 2\) - step1: Multiply the terms: \(24x^{3}\times x^{2}\) - step2: Multiply the terms: \(24x^{3+2}\) - step3: Add the numbers: \(24x^{5}\) Calculate or simplify the expression \( (x^2)^3 + x^3 \). Simplify the expression by following steps: - step0: Solution: \(\left(x^{2}\right)^{3}+x^{3}\) - step1: Multiply the exponents: \(x^{2\times 3}+x^{3}\) - step2: Multiply the numbers: \(x^{6}+x^{3}\) Calculate or simplify the expression \( (4*x^2*y^3)^2 \). Simplify the expression by following steps: - step0: Solution: \(\left(4x^{2}y^{3}\right)^{2}\) - step1: Use the properties of exponents: \(4^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}\) - step2: Evaluate the power: \(16x^{4}y^{6}\) Calculate or simplify the expression \( (3*b^3)^2 \). Simplify the expression by following steps: - step0: Solution: \(\left(3b^{3}\right)^{2}\) - step1: Use the properties of exponents: \(3^{2}\left(b^{3}\right)^{2}\) - step2: Evaluate the power: \(9b^{6}\) Calculate or simplify the expression \( (5*x^2)^2*(2*x^(-1))^3 \). Simplify the expression by following steps: - step0: Solution: \(\left(5x^{2}\right)^{2}\left(2x^{-1}\right)^{3}\) - step1: Reduce the numbers: \(25x\times 8\) - step2: Multiply the numbers: \(200x\) Calculate or simplify the expression \( (4*x^2*y^2)*(2*x*y^3)^3 \). Simplify the expression by following steps: - step0: Solution: \(4x^{2}y^{2}\left(2xy^{3}\right)^{3}\) - step1: Rewrite the expression: \(4x^{2}y^{2}\times 8x^{3}y^{9}\) - step2: Multiply the numbers: \(32x^{2}y^{2}x^{3}y^{9}\) - step3: Multiply the terms: \(32x^{5}y^{2}\times y^{9}\) - step4: Multiply the terms: \(32x^{5}y^{11}\) Calculate or simplify the expression \( 4*a^2*2*a \). Simplify the expression by following steps: - step0: Solution: \(4a^{2}\times 2a\) - step1: Multiply the terms: \(8a^{2}\times a\) - step2: Multiply the terms: \(8a^{2+1}\) - step3: Add the numbers: \(8a^{3}\) Here are the simplified results for each expression: a) \( (x^2)^3 + x^3 \) - Simplification: \[ (x^2)^3 = x^{6} \quad \text{so,} \quad x^{6} + x^{3} \] Result: \( x^{6} + x^{3} \) b) \( 3x^3 \times 4x^2 \times 2 \) - Simplification: \[ 3 \times 4 \times 2 = 24 \quad \text{and} \quad x^3 \times x^2 = x^{5} \] Result: \( 24x^{5} \) c) \( 4a^2 \times 2a \) - Simplification: \[ 4 \times 2 = 8 \quad \text{and} \quad a^2 \times a = a^{3} \] Result: \( 8a^{3} \) d) \( 10y^4 + 2y^3 \) - This expression is already simplified. Result: \( 10y^{4} + 2y^{3} \) e) \( (3b^3)^2 \) - Simplification: \[ (3b^3)^2 = 3^2 \times (b^3)^2 = 9b^{6} \] Result: \( 9b^{6} \) f) \( (4x^2y^3)^2 \) - Simplification: \[ (4^2)(x^2)^2(y^3)^2 = 16x^{4}y^{6} \] Result: \( 16x^{4}y^{6} \) g) \( (5x^2)^2 \times (2x^{-1})^3 \) - Simplification: \[ (5^2)(x^2)^2 \times (2^3)(x^{-3}) = 25x^{4} \times 8x^{-3} = 200x^{1} = 200x \] Result: \( 200x \) h) \( (4x^2y^2) \times (2xy^3)^3 \) - Simplification: \[ (2^3)(x^1)^3(y^3)^3 = 8x^{3}y^{9} \quad \text{and} \quad 4x^2y^2 \times 8x^{3}y^{9} = 32x^{5}y^{11} \] Result: \( 32x^{5}y^{11} \) i) \( (x y^{2}) \times (x y^{2}) \) - Simplification: \[ (x^1)(x^1)(y^2)(y^2) = x^{2}y^{4} \] Result: \( x^{2}y^{4} \) In summary, the simplified results are: - a) \( x^{6} + x^{3} \) - b) \( 24x^{5} \) - c) \( 8a^{3} \) - d) \( 10y^{4} + 2y^{3} \) - e) \( 9b^{6} \) - f) \( 16x^{4}y^{6} \) - g) \( 200x \) - h) \( 32x^{5}y^{11} \) - i) \( x^{2}y^{4} \)