Yes, SDXC cards work on SDHC host devices. The image below shows the host device and the memory cards supported in detail.
Cards and host devices
-SDUC memory cards must only be used with SDUC host devices.
-SDXC memory cards can be used with SDXC and SDUC host devices.
-SDHC memory cards can be used with SDHC, SDXC and SDUC host devices.
-SD memory cards can be used with SD, SDHC, SDXC and SDUC host devices.
Additional info on cards and host devices
-SDUC Host Devices can use SD, SDHC, SDXC and SDUC memory cards.
-SDXC Host Devices can use SD, SDHC and SDXC memory cards.
-SDHC Host Devices can use both SD and SDHC memory cards.
-SD Host Devices can only use SD memory cards.
*Source: SD Association