https://file.aiquickdraw.com/mathbot/file/1727162274308w7kppd28.jpg

The question in the image asks to find the result of:

\[
(0.5)^3 \cdot 2 \cdot \left(\frac{1}{4}\right)^{-2}
\]

Let's break this down step by step:

### Step 1: Simplify \((0.5)^3\)
\[
0.5 = \frac{1}{2}, \quad \left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8}
\]

### Step 2: Simplify \(\left(\frac{1}{4}\right)^{-2}\)
Using the property \( \left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n \), we get:
\[
\left(\frac{1}{4}\right)^{-2} = \left(\frac{4}{1}\right)^2 = 4^2 = 16
\]

### Step 3: Multiply the results
Now, multiply all the terms:
\[
\frac{1}{8} \cdot 2 \cdot 16 = \frac{1}{8} \cdot 32 = \frac{32}{8} = 4
\]

Thus, the result is:

\[
\boxed{4}
\]

Would you like further details on any step or have more questions?

Here are 5 related questions you might find interesting:
1. How do you simplify expressions with negative exponents?
2. What is the general rule for raising fractions to a power?
3. How can you simplify expressions that involve multiplying powers of different numbers?
4. How do you handle different bases when simplifying exponential expressions?
5. How can we extend these concepts to work with variables in algebraic expressions?

**Tip:** Remember that multiplying powers of fractions follows the same rules as regular numbers—work with both the numerators and denominators step by step.

Hasil perpangkatan dari (0,5)^3 . 2 . (1/4)^(-2) adalah ....

Learn how to solve the exponentiation problem involving (0.5)^3, multiplication by 2, and the negative exponent (1/4)^(-2). This covers key concepts such as handling negative exponents and simplifying fractions. Suitable for high school students in Grades 9-11.

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