We improve the large sieve inequality with
k
t
h
k^{\mathrm {th}}
-power moduli, for all
k
≥
4
k\ge 4
. Our method relates these inequalities to a variant of Waring’s problem with restricted
k
t
h
k^{\mathrm {th}}
-powers. Firstly, we input a classical divisor bound on the number of representations of a positive integer as a sum of two
k
t
h
k^{\mathrm {th}}
-powers. Secondly, we apply Marmon’s bound on the number of representations of a positive integer as a sum of four
k
t
h
k^{\mathrm {th}}
-powers. Thirdly, we use Wooley’s Vinogradov mean value theorem with arbitrary weights. Lastly, we state a conditional result, based on the conjectural Hardy-Littlewood formula for the number of representations of a large positive integer as a sum of
k
+
1
k+1
k
t
h
k^{\mathrm {th}}
-powers.