Use rational exponents

Question

Use rational exponents to simplify the expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers.

⁹ √x ⁴ • √x

Answer 1

     ___     ____
⁹ √x ⁴ • √x

 

First term is x raised to the 4th power, then taking the 9th root of that result.

Second term is just x raised to the 1/2 power or the 2nd root of x.

x^4/9 (x ^1/2) = x ^{(4/9 + 1/2)}

Since 4/9 + 1/2 = 8/18 + 9/18 = 17/18,

x ^{(4/9 + 1/2)} = x ^17/18

     _____
¹⁸√x¹⁷