What is the units' digit of the following expression (13)^5*(15)^4*(17

Question

What is the units' digit of the following expression (13)^5*(15)^4*(17)^5?

A. 0
B. 1
C. 3
D. 5
E. 9

chetan2u · Accepted Answer

We do not have to do any calculations or find units digit of remaining numbers... 
all three terms - 13,15,17 - are ODD and since the PRODUCT contains 5, the units digit of the product will remain 5

D

bimalr9 · Answer

The unit digit of  3^5  is 3.
The unit digit of  5^4  is 5
the unit digit of  7^5  is 7.

The unit digit of  3*5*7  is 5.
Answer D.

abrahamic · Answer

This might help:
Of the (13)^5*(15)^4*(17)^5, 
 (13)^5 = Odd
 (17)^5 = Odd
 (15)^4 = Unit digit of 5
 5*Odd = Unit of 5

ScottTargetTestPrep · Answer

Since we need the units digit of (13)^5*(15)^4*(17)^5, we are really looking for the units digit of:

(3)^5 * (5)^4 * (7)^5

The pattern for units digits of powers of 3 is 3-9-7-1, so when 3 is raised to an exponent that is a multiple of 4, the units digit is 1. Thus, 3^4 has units of 1, and so 3^5 has a units digit of 3.

Since a base of 5 raised to an exponent will always end in 5, 5^4 has a units digit of 5.

Next, the pattern for units digits of powers of 7 is 7-9-3-1, so when 7 is raised to an exponent that is a multiple of 4, the units digit is 1. Thus, 7^4 has units of 1 and 7^5 has a units digit of 7.

Now we multiply the three units digits that we have just obtained. Since 3 x 5 x 7 = 105 (with a units digit of 5), the units digit of (3)^5 * (5)^4 * (7)^5 must also be 5, and thus the units digit of (13)^5 * (15)^4 * (17)^5 is 5.

Answer: D

HolaMaven · Answer

Using Cyclic rule of unit digit we can find the unit digit of any number written in exponent form. Following steps can be of help.
If a number is written as  k^{x} 
Divide the power by 4 and check for remainder.
If remainder =1, unit digit of the answer is going to be same as unit digit of 'k'
If remainder =2, unit digit is going to be the unit digit of  k^{2} 
If remainder =3, unit digit is going to be the unit digit of  k^{3} 
If remainder =0, unit digit is going to be the unit digit of  k^{4}

For example: To find unit digit of  2017^{35} 
Divide the power,35, by 4. Check the remainder
 \frac{35}{4} gives remainder 3
Thus  2017^{35} will have last digit same as last digit of  2017^{3} 
7*7*7 gives last digit as 3
Thus answer of above example is 3.

Fdambro294 · Answer

Concept: whenever a number is divisible by 5, the units digit must be either:

0 or 5

Since (15)^3 is a factor in the multiplication chain, the result must be a multiple of 5.

Thus, only A or D is a possible answer

Concept 2: in order to have a units digit of 0 (a “trailing zero”) the prime factorization of the product needs to include at least 1 prime factor pair of (2 x 5)

Since all 3 Bases are ODD, the result must be ODD, and can NOT end in a units digit of 0

Answer must be (d) 5

Posted from my mobile device

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What is the units' digit of the following expression (13)^5(15)^4(17

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