What is the value of 10^8 - 6^7?

\(10^8\) ends with 0; \(6^7\) ends with 6

Difference will provide 4 at the units place

Answer = A

We can attack this question a bit differently using some properties

Rule 1

10^n power = 1 with n amount of zeros... 10^2 is 100 (2 zero) 10^5 100,000 (five zero)

so

100000000 -6^7

Rule 2

What is unit digits of 6? 6 is a special number 6^n will always have a units digit of 6 so the units digits of the answer must be 4

Thus
"A"

\(10^8\) Will have units digit as 0
\(6^7\) Will have units digit as 6

Now, \(10^8 - 6^7\) will have units digit as \(0 - 6 = 4\)

Among the given options only (A) satisfies, so that is the answer...

Since we know that the GMAT would not expect us to carry out the computation of the exact value of 10^8 - 6^7, we can focus on the units digits of the resulting difference.

When we raise 10 to any power, the units digit of the answer is always 0. For example, 10^2 = 100 and 10^4 = 10,000. Similarly, the units digit of 6 raised to any power is 6. For example, 6^2 = 36, 6^3 = 216, etc.
In this problem, the units digit of 10^8 will be 0 and the units digit of 6^7 will be 6. Thus, subtracting 6 from 10 (after 0 “borrows” a 1 from the tens digit) will result in a units digit of 4. Therefore, 10^8 - 6^7 must be equal to 99,720,064 since that is the only answer choice with a units digit of 4.

Answer: A

OA:A

Unit digit of \(10^8\) is \(0\) and unit digit of \(6^7\) is \(6\), Unit digit of expression \(10^8 - 6^7\) will be \(10-6 = 4\), as \(10^8>6^7\).
Only Option A has 4 at unit's digit.

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