Liquid wrote:

I can't count the number of questions I've come across of this nature:

What is the units digit of (9^3)(4^5)(6^3)?

any ideas as to how I can solve questions like this?

In these type of questions it helps to remember that all number from 1-9 when raised to a power have a cyclicity for the unit digits.

For example taking 4 for instance : 4,16,64,256.... As seen, powers of 4 repeat their unit digits at an interval of 2.

Similarly for 9 : 9,81,729,..... powers of 9 Also repeats their units digit at an interval of 2.

For 6: 6,36,216..... The units digit of powers of 6 remain the same...

Thus, for the question we get that the units digit of 9^3 = 9, 4^5 = 4, 6^3 = 6.

The multiplication of 9,4, as units digit would give 36 as the units digit and subsequent multiplication with a number with unit's digit 6 will also give 6 as the unit's digit.

TIP: Try to memorize the intervals at which the exponents of numbers from 1-9 repeat their unit's digits.

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Paras.

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