The problem in the image asks to solve the following expression:

$\left(\frac{1}{2}\right)^2 \times \left(\frac{1}{2}\right)^5$

This is a multiplication of powers with the same base. The rule for multiplying powers with the same base is:

$a^m \times a^n = a^{m+n}$

So, applying this to the given expression:

$\left(\frac{1}{2}\right)^2 \times \left(\frac{1}{2}\right)^5 = \left(\frac{1}{2}\right)^{2+5} = \left(\frac{1}{2}\right)^7$

Thus, the correct answer is C: $\left(\frac{1}{2}\right)^7$.

Would you like further details or have any other questions?

Here are 5 related questions for further practice:

1. Simplify $\left(\frac{3}{4}\right)^2 \times \left(\frac{3}{4}\right)^4$.
2. What is the result of $\left(\frac{2}{3}\right)^3 \times \left(\frac{2}{3}\right)^2$?
3. Simplify $\left(5\right)^3 \times \left(5\right)^6$.
4. How do you simplify $\left(x^4\right) \times \left(x^5\right)$?
5. Simplify $\left(\frac{5}{6}\right)^4 \times \left(\frac{5}{6}\right)$.

Tip: When multiplying expressions with the same base, just add the exponents!