4⁵÷4-² 5³+3⁵ 5⁰-1⁴ (14.2)⁴×(14.2)¼ (14.2)⁴+(14.2)¼

Here are the solutions to the expressions:

1) $4^5 \div 4^{-2}$ Step 1: Apply the exponent rule for division: $a^m \div a^n = a^{m-n}$. $4^5 \div 4^{-2} = 4^{5 - (-2)}$ Step 2: Simplify the exponent. $4^{5+2} = 4^7$ Step 3: Calculate the value. $4^7 = 16384$ Final answer: $\boxed{16384}$

2) $5^3 + 3^5$ Step 1: Calculate $5^3$. $5^3 = 5 \times 5 \times 5 = 125$ Step 2: Calculate $3^5$. $3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$ Step 3: Add the results. $125 + 243 = 368$ Final answer: $\boxed{368}$

3) $5^0 - 1^4$ Step 1: Calculate $5^0$. Any non-zero number raised to the power of 0 is 1. $5^0 = 1$ Step 2: Calculate $1^4$. 1 raised to any power is 1. $1^4 = 1$ Step 3: Subtract the results. $1 - 1 = 0$ Final answer: $\boxed{0}$

4) $(14.2)^4 \times (14.2)^{1/4}$ Step 1: Apply the exponent rule for multiplication: $a^m \times a^n = a^{m+n}$. $(14.2)^4 \times (14.2)^{1/4} = (14.2)^{4 + \frac{1}{4}}$ Step 2: Add the exponents. $4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4}$ Step 3: Write the result in exponential form. $(14.2)^{\frac{17}{4}}$ Final answer: $\boxed{(14.2)^{\frac{17}{4}}}$

5) $(14.2)^4 + (14.2)^{1/4}$ Step 1: Calculate $(14.2)^4$. $(14.2)^4 = 40658.6756$ Step 2: Calculate $(14.2)^{1/4}$ (the fourth root of 14.2). $(14.2)^{1/4} \approx 1.9410$ Step 3: Add the results. $40658.6756 + 1.9410 \approx 40660.6166$ Rounding to two decimal places: $40660.62$ Final answer: $\boxed{40660.62}$