Somewhat smooth numbers in short intervals

We use exponent pairs to establish the existence of many $$x^a$$ -smooth numbers in short intervals $$[x-x^b,x]$$ , when $$a>1/2$$ . In particular, $$b=1-a-a(1-a)^3$$ is admissible. Assuming the exponent-pairs conjecture, one can take $$b=(1-a)/2+\epsilon $$ . As an application, we show that $$[x-x^{0.4872},x]$$ contains many practical numbers when x is large.