Final answer:
To evaluate the expression, simplify the numerator and the denominator separately. Then divide the numerator by the denominator. The final expression is 15 * 3^(-1) * sqrt(5)^(-5).
Step-by-step explanation:
To evaluate the expression, we can simplify it step by step.
First, let's simplify the numerator: 3 * sqrt(5) * sqrt(5). Since the square root of a number times itself is just the number, we can simplify sqrt(5) * sqrt(5) to just 5. So the numerator becomes 3 * 5 which equals 15.
Next, let's simplify the denominator: 3 * sqrt(5)^5. The fifth power of the square root of 5 is the same as the square root of 5 raised to the power of 5. So the denominator becomes 3 * (sqrt(5))^5. Since the power over a power rule states that when we raise a power to another power, we multiply the exponents, the denominator simplifies to 3 * sqrt(5)^(5*1) which equals 3 * sqrt(5)^5.
Now we can rewrite the expression as 15 / (3 * sqrt(5)^5). To divide a fraction, we can multiply by the reciprocal of the denominator. So the expression simplifies to 15 * (3 * sqrt(5)^5)^(-1).
Finally, we can simplify the expression further by applying the power rule again: 15 * 3^(-1) * (sqrt(5)^5)^(-1). The reciprocal of a number raised to a power is the same as the number raised to the negative power, so we can rewrite the expression as 15 * 3^(-1) * sqrt(5)^(-5). This is the simplified form of the expression.