Given software support, any SDHC card reader is capable of reading SDXC cards.
From Secure Digital # SDXC - Wikipedia:
Compatibility with SDHC
[...] SDHC host devices will accept SDXC cards that follow Version 3.0, since the interface is identical, but the following issues may affect usability:
SDXC cards are pre-formatted with Microsoft's proprietary and patented exFAT file system, which the host device might not support. [...] FAT32-formatted SDXC cards can be used in a host device built for SDHC if the host device can handle 64GB and larger volumes.
SDHC host devices will not test the new capability bits defined for SDXC 4.0 cards. It will therefore not be able to use the new features of SDXC, such as transfer speeds above UHS104 (104MB/s).
SD/SDHC/SDXC Specifications and Compatibility confirms this:
SDXC cards will work in SDHC compatible readers (not SD readers) if the computer OS supports exFAT. For more information on exFat see: Operating Systems that support the exFAT File System
The provided link contains information on how to obtain software support for Windows and OS X. For BSD or Linux, exfat - Free exFAT file system implementation - Google Project Hosting may be used.
Here's an article with working link archived version without images. And also a summary of how you do this:
Start DiskPart by opening Start menu and typing in diskpart in the search. After giving DiskPart permission to start with administrative privileges, you will be in a console window with DISKPART> prompt.
Deleting partitions
Type LIST DISK to find out what disk you need to change. Note that you are looking for a disk with the same number as in the Disk Management tool, so in OP's case, it's Disk 1.
Next you need to select the disk you wish to work on. Type SELECT DISK 1. Make sure the correct disk is selected by typing LIST DISK again.
Now, you need to select the partition you wish to remove. Type LIST PARTITION to see a list of all partitions. To select the first one, type SELECT PARTITION 1.
To remove the partition, type DELETE PARTITION.
Creating partitions
To create a partition, you can either proceed by using the Disk Management tool, or type CREATE PARTITION PRIMARY. This creates a partition that fills the free space. If you wish to create a partition of specific size, you need to type CREATE PARTITION PRIMARY SIZE=NNN where NNN is the partition size in MB.
You can get more information about the various options by typing HELP CREATE PARTITION and/or HELP CREATE PARTITION PRIMARY.
Exiting DiskPart
Either type EXIT or press Ctrl+C.
Additional notes
While this works for many SD cards (and other media), for SD cards specifcially, it is recommended to use SD formatter from SD Association. It will not remove all partitions, but will ensure that any content security-related parts of the card are left intact.
Although not being asked, this method may not work for USB sticks. I have 'bricked' USB sticks by partitioning them on Linux or writing ISO images to them, and to date, I haven't found a way to fix them.
Best Answer
I have the same problem. I've successfully installed Ubuntu 14.04 on USB, and it booted fine. However, when trying to install onto microSD card (through built-in reader) Ubuntu installs really slow, and just freezes before completing installation. Maybe it's something to do with SD cards themselves, because when I've tried to install Android-x86, it said installed successfully, but upon booting, it showed up in the boot device selection screen, but had a boot error. I've just been sticking to USBs. They're bulky, but hey, they work.