2(36) with an exponent of negative one half added by 6 with an exponent of negative one.

The expression can be written as:

\[
2(36)^{-\frac{1}{2}} + 6^{-1}
\]

Let's solve it step by step:

1. **First term:** \( 36^{-\frac{1}{2}} \) means the square root of 36, taken to the negative power. The square root of 36 is 6, and the negative exponent makes it \(\frac{1}{6}\). Thus:

   \[
   36^{-\frac{1}{2}} = \frac{1}{6}
   \]

   Now multiply by 2:

   \[
   2 \times \frac{1}{6} = \frac{2}{6} = \frac{1}{3}
   \]

2. **Second term:** \( 6^{-1} = \frac{1}{6} \).

Now, add the two terms together:

\[
\frac{1}{3} + \frac{1}{6}
\]

To add fractions, we need a common denominator:

\[
\frac{1}{3} = \frac{2}{6}
\]

So:

\[
\frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}
\]

Thus, the final result is:

\[
\frac{1}{2}
\]

Would you like further details or clarifications?

Here are 5 related questions:

1. What is the general rule for handling negative exponents?
2. How do you simplify expressions involving fractional exponents?
3. What is the process for adding fractions with different denominators?
4. How does multiplying by a negative exponent affect the outcome of a power?
5. How can you calculate roots and powers mentally?

**Tip:** When dealing with negative exponents, always think of them as reciprocals to simplify the process.

Learn how to simplify the expression 2(36)^(-1/2) + 6^(-1) using properties of exponents and fractions. This problem explores concepts such as negative exponents and fraction addition, suitable for students in Grades 8-10.

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