What's 4 to the power of 5.5

4^5.5  =  4^{5 + .5}  =  4^{5 + 1/2}

    =  4⁵ x 4^1/2            (Adding exponents means multiplying bases.)

    =  4⁵ x √4               (A 1/2 exponent is a square root.)

    =  1024 x 2

    =  2048

Why don't you try & use any calculator with a X^Y key & get the answer?

4^5.5 =2048