### Instruction: Calculate $\left(\frac{1}{a}\right)^4 \cdot 2 \cdot a^4+a^{2+1-3}$ when $a=42$.### Response: I need to evaluate this expression for a given value of a, so I can start by plugging in a=42 wherever it appears.
I get $\left(\frac{1}{42}\right)^4 \cdot 2 \cdot 42^4+42^{2+1-3}$.
Next, I can simplify the exponents using the rules of powers.
For the first term, I can write $\left(\frac{1}{42}\right)^4 \cdot 2 \cdot 42^4 = \frac{1^4}{42^4} \cdot 2 \cdot 42^4 = \frac{1}{42^4} \cdot 2 \cdot 42^4$.
Then, I can cancel out the 42^4 terms in the numerator and denominator, leaving me with $\frac{1}{42^4} \cdot 2 \cdot 42^4 = 2$.
For the second term, I can simplify the exponent by adding and subtracting the numbers inside the parentheses.
I get $42^{2+1-3} = 42^0$.
Any number raised to the zero power is 1, so $42^0 = 1$.
Now, I have $2 + 1$.
Finally, I can add these two numbers to get the final answer.