Solve (ab/2x)³: Cubing a Complex Algebraic Fraction

To solve this problem, we'll follow these steps:

• Step 1: Express the given expression $\left(\frac{a \times b}{2 \times x}\right)^3$ using exponent rules for fractions.
• Step 2: Apply the cube power to both the numerator and the denominator separately.
• Step 3: Simplify the expression and compare it to the provided choices.

Now, let's work through each step:

Step 1: We have the expression $\left(\frac{a \times b}{2 \times x}\right)^3$. According to the power of a fraction rule, $\left(\frac{m}{n}\right)^p = \frac{m^p}{n^p}$, we can raise the numerator and denominator to the power of 3 separately.

Step 2: Apply the cube power:

• Numerator: $(a \times b)^3 = a^3 \times b^3$
• Denominator: $(2 \times x)^3 = 2^3 \times x^3 = 8 \times x^3$

Step 3: Combine these results:

The expression simplifies to $\frac{a^3 \times b^3}{8 \times x^3}$.

Comparing it to the given choices, we find that this matches Choice 1: $\frac{a^3 \times b^3}{8 \times x^3}$.

Therefore, the solution to the problem is $\frac{a^3 \times b^3}{8 \times x^3}$.