Simplify: a. (14.2)3 + (14.2)3/4, 1. (14.2)4 x (14.2)4

a) Step 1: Identify the expression and apply the exponent rule $a^m \times a^n = a^{m+n}$. The expression is $(14.2)^4 \times (14.2)^{\frac{1}{4}}$. $(14.2)^4 \times (14.2)^{\frac{1}{4}} = (14.2)^{4 + \frac{1}{4}}$ Step 2: Calculate the sum of the exponents. $4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4}$ Step 3: Write the simplified expression. $(14.2)^{\frac{17}{4}}$ The simplified expression is \boxed{(14.2)^{\frac{17{4}}}}.

b) Step 1: Identify the expression. The expression is $(14.2)^2 + (14.2)^{\frac{1}{4}}$. Step 2: Calculate the value of the first term, $(14.2)^2$. $(14.2)^2 = 14.2 \times 14.2 = 201.64$ Step 3: Calculate the value of the second term, $(14.2)^{\frac{1}{4}}$. $(14.2)^{\frac{1}{4}} \approx 1.9406$ Step 4: Add the values of the two terms. $201.64 + 1.9406 = 203.5806$ The value of the expression is $\boxed{203.5806}$.