To solve the equation 5/3 to the power of 2×3/5 to the power of -3 and find the value of x-2, let's break down the problem step by step:

Step 1: Simplify the exponents
First, let's simplify the exponents in the equation. We have:
2×3/5 to the power of -3

To simplify this, we need to apply the power of a power rule, which states that (a^b)^c = a^(b×c). Applying this to our equation, we get:
2×3/5 to the power of -3 = 2×(3/5)×(-3)

Now we can simplify the exponent:
2×(3/5)×(-3) = 2×(3×(-3))/5 = 2×(-9)/5 = -18/5

Step 2: Evaluate 5/3 to the power of -18/5
Next, let's evaluate 5/3 to the power of -18/5. To simplify this, we can use the power of a quotient rule, which states that (a/b)^c = a^c/b^c.

Applying this rule to our equation, we have:
(5/3)^(-18/5) = 5^(-18/5)/3^(-18/5)

Now, let's simplify the numerator and denominator separately:
Numerator: 5^(-18/5)
To simplify this, we can use the power of a power rule, which states that (a^b)^c = a^(b×c). Applying this to our equation, we get:
5^(-18/5) = (5^(-1))^(-18/5) = (1/5)^(-18/5)

Now, let's apply the power of a quotient rule again:
(1/5)^(-18/5) = 1^(-18/5)/5^(-18/5) = 1/5^(-18/5)

Denominator: 3^(-18/5)
Using the same steps as above, we can simplify 3^(-18/5) to 1/3^(-18/5).

Step 3: Combine the simplified numerator and denominator
Now we can combine the simplified numerator and denominator:
(1/5^(-18/5))/(1/3^(-18/5)) = (1/5^(-18/5))×(3^(-18/5)/1)

To simplify further, we can multiply the fractions:
(1/5^(-18/5))×(3^(-18/5)/1) = 1×3^(-18/5)/(5^(-18/5)×1)

Step 4: Evaluate the powers of 3 and 5
Now, let's evaluate the powers of 3 and 5 separately:
3^(-18/5) = 1/3^(18/5)
5^(-18/5) = 1/5^(18/5)

Step 5: Simplify the expression
Finally, let's simplify the expression by substituting the evaluated powers back into the equation:
1×(1/3^(18/5))/(1/5^(18/5)×1) = 1