Solve for X: (2/105)^x Expression with Product Denominator

To solve this problem, we need to express $\left(\frac{2}{3 \times 5 \times 7}\right)^x$ by applying the rule for powers of a fraction.

Using the exponent rule $\left(\frac{a}{b}\right)^x = \frac{a^x}{b^x}$, we proceed as follows:

• Step 1: Express the numerator and denominator with the exponent $x$.
  The expression $\left(\frac{2}{3 \times 5 \times 7}\right)^x$ becomes $\frac{2^x}{(3 \times 5 \times 7)^x}$.
• Step 2: Apply the power of a product rule to the denominator.
  This results in $(3 \times 5 \times 7)^x = 3^x \times 5^x \times 7^x$.
• Step 3: Substitute back into the fraction from Step 1.
  We get $\frac{2^x}{3^x \times 5^x \times 7^x}$.

Therefore, the original expression $\left(\frac{2}{3 \times 5 \times 7}\right)^x$ simplifies to $\frac{2^x}{3^x \times 5^x \times 7^x}$.

The correct answer is: $\frac{2^x}{3^x \times 5^x \times 7^x}$.