https://file.aiquickdraw.com/mathbot/file/17273369877265cu0llxp.jpg

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!

Learn how to solve the expression (1/2)^2 × (1/2)^5 by applying exponent rules. This problem focuses on exponentiation and the rule of adding exponents when multiplying like bases, suitable for students in Grades 7-9.

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