81^3 + 27^4 is equivalent to which of the following expressions?

Question

81^3 + 27^4  is equivalent to which of the following expressions?

I.  (3^{12})(2)

II.  (9^6)(2)

III.  9^{12}

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

Lampard42 · Answer

The expression can be simplified to (3^4)^3 + (3^3)^4 = 3^12+3^12 = 2(3^12). Part two is same as part 1. So option D

Posted from my mobile device

KSBGC · Answer

Given,

81^3 + 27^4

(3^4)^3 + (3^3)^4

3^12 + 3^12

3^12( 1 + 1 )

3^12 * 2

Here we have to observe that 3 and 2 are different primes.

another way to express this term.

(3^2)^6 * 2

(9)^6 * 2

D is the correct answer.

LeoN88 · Answer

Question Stem: 3^12 + 3^12

I Yes- 2* 3^12

II Yes- (9^6)= 3^12

III There is no factor for 2 here.
Only I and II  (D)

ashu2526 · Answer

81^3 + 27^4

Case1: (3)^12 + (3)^12 = 3^12(1+1) = 3^12(2) 
This I

Case2: (9)^6 + (9)^6 = 9^6(2)
Thus II

Hence option D

Prep Toolkit