Final answer:
The expression 'r to the power of 9/5' can be rewritten as the fifth root of r to the ninth power, which is another form of expressing fractional exponents.
Step-by-step explanation:
When we talk about expressions like r to the power of 9/5, we're dealing with fractional exponents. Understanding this concept can be made simpler by looking at integer powers. For instance, the expression 4³ means 4 multiplied by itself three times (4x4x4). Conversely, when dealing with fractional exponents, the numerator indicates the power and the denominator indicates the root. So, r to the power of 9/5 means that r is raised to the 9th power and then the fifth root is taken.
Therefore, another way to express r to the power of 9/5 is the fifth root of r to the ninth power (√(r⁹)). This operation adheres to the rules of exponents, where multiplying two exponents with the same base is equivalent to adding the exponents, and where a fractional exponent indicates both a power and a root.