Simplifying (32/243) raised to the power -3/5

To simplify (32/243) raised to the power -3/5, we need to follow the steps given below:

Step 1: Convert the given fraction into a power of prime factors

32/243 can be written as (2^5)/(3^5)

Step 2: Apply the power rule

((2^5)/(3^5))^(-3/5) can be written as ((2^5)^(-3/5))/((3^5)^(-3/5))

Step 3: Simplify the exponents

((2^5)^(-3/5))/((3^5)^(-3/5)) = (2^(-3))*(3^3)

Step 4: Simplify the expression

(2^(-3))*(3^3) can be written as (27/8)

Therefore, (32/243)^(-3/5) = 27/8.

Explanation:

The given expression is to simplify (32/243) raised to the power -3/5. To simplify it, we first convert the given fraction into a power of prime factors. Then, we apply the power rule and simplify the exponents. Finally, we simplify the expression to get the simplified form of the given expression.

In this way, we can simplify any expression involving exponents and fractions.