Question

Simplify:

(1) 7²⁸ *7¹⁵*1/7¹³

(2) (1/3)⁴*(-27/4)²*(-8/3)²

Answer 1

(1) 7²⁸ *7¹⁵*1/7¹³

= 7²⁸ *7¹⁵*7^-13

= 7^(28+15-13) [when the bases are equal, the powers are added under a base]

= 7^(43-13)

= 7^{30 Ans.}


(2) (1/3)⁴*(-27/4)²*(-8/3)²

= [(1/3)²]²*(-27/4)²*(-8/3)²

= (1/9)²*(-27/4)²*(-8/3)²

= {(1/9)*(-27/4)*(-8/3)}² }[ when the powers are equal, all bases are multiplied under a power ]

= (1/9* 27/4*8/3)²

= (3/4*8/3)²

= (2)² =​​​​​​​ 4 Ans.