Question

What does a rational exponent, such as 9^(5/2), mean?

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf 9^{(5)/(2)} = \sqrt[\sf 2]{\sf 9^5}$}`

`\Large \text{$ \sf 9^{(5)/(2)} = \sqrt[\sf 2]{\sf (3^2)^5}$}`

`\Large \text{$ \sf 9^{(5)/(2)} = \sqrt[\sf 2]{\sf 3^(10)}$}`

`\Large \text{$ \sf 9^{(5)/(2)} = \sqrt[\sf 2]{\sf (3^(5))^2}$}`

`\Large \text{$ \sf 9^{(5)/(2)} = 3^5$}`

`\Large \boxed{\boxed{\text{$ \sf 9^{(5)/(2)} = 243$}}}`

Answer 2

A rational exponent like 9^(5/2) means raising 9 to the 5th power and then taking the square root of the result. The exponent indicates the power to which the number is raised, and the denominator indicates the root that is applied thereafter.

Step-by-step explanation:

A rational exponent is an exponent that is a fraction, where the numerator represents the power and the denominator represents the root. For instance, 95/2 means that 9 is to be raised to the power of 5 and then the square root (since 2 is the denominator) of that result is to be taken. To calculate this, you can either first take the square root of 9, which is 3, and then raise the result to the 5th power (35), or raise 9 to the 5th power and then take the square root of the result. This concept helps in simplifying expressions and solving equations involving fractional powers.