Final answer:
In cases of intentional discrimination on the basis of gender by a state government, the appropriate standard is intermediate scrutiny, which requires the government to provide an exceedingly persuasive justification.
Step-by-step explanation:
The burden and standard that apply in a case charging intentional discrimination by a state government on the basis of gender requires the government to show an exceedingly persuasive justification for the unequal treatment. This falls under the intermediate scrutiny standard, as gender discrimination is not subjected to the strictest form of judicial review, which is strict scrutiny, nor is it evaluated under the more lenient rational basis test. Therefore, the correct answer is: The government must show an exceedingly persuasive justification to pass the intermediate scrutiny test.