Solve for x in (3/10)^x: Complete the Exponential Expression

Insert the corresponding expression:

$\left(\frac{3}{2\times5}\right)^x=$

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

• Step 1: Identify the given expression.
• Step 2: Apply the exponent rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ to distribute $x$ to numerator and denominator.
• Step 3: Simplify the denominator expression by distributing exponent $x$ to each factor.

Now, let's work through each step:
Step 1: We have the original expression $\left(\frac{3}{2 \times 5}\right)^x$.
Step 2: Apply the rule to get $\frac{3^x}{(2 \times 5)^x}$.
Step 3: Expand the denominator: $(2 \times 5)^x = 2^x \times 5^x$. This leads us to $\frac{3^x}{2^x \times 5^x}$.

Therefore, the solution to the problem is $\frac{3^x}{2^x \times 5^x}$.