Yes, I agree that 0.777 and 7/9 are equivalent.
The decimal 0.777 represents the fraction 7/9 in base 10. In base 10, the digit 7 in the tenths place represents 7/10, the digit 7 in the hundredths place represents 7/100, and the digit 7 in the thousandths place represents 7/1000. When these values are added together, the result is 7/10 + 7/100 + 7/1000, which simplifies to 7/10 + 7/100 + 7/1000 = 7/10 + 7/100(10/10) + 7/1000(10/10)(10/10) = 7/10 + 7/10 + 7/10 = 21/10 = 7/3.
Since 7/3 can be simplified to 7/9, 0.777 is equivalent to 7/9.
Therefore, Brandon's statement that 0.777 and 7/9 are equivalent is correct.