Question

Solve all of these questions.

There are 10 of them.

Answer 1

you have to configure all the possible applications of indices.

Answer 2

1) [(5/4)^3]^4
= (5/4)^12


2) [(-1/3)^7]^9 × 3^60
=(-1/3)^7×9 × 3^60
= (-1/3)^63 × 3^60
= (-3)^-63 × 3^60
= -1(3)^-63×3^60
=-1(3)^-63+60
=-3^-3
=(-1/3)^3
=-1/27


3) (3^8)^4 × 1/(2^9)^4
= 3^8×4 × 1/2^9×4
= 3^32 × 1/2^36
=3^32/2^36


4)(11/20)^25 ÷ (11/20)^34
= (11/20)^25-34
=(11/20)^-9
=(20/11)^9


5) (3/7)^-1 × (7/3)^-1
= 7/3 × 3/7
= 1


6)6^19 × 6^18 ×1/6^30
=6^19×6^18×6^-30
=6^19×6^18+(-30)
=6^19×6^-12
=6^19+(-12)
=6^7


7) 6^0 - 9^0 - 10^0
= 1-1-1
=1-2
=-1


8) (3^-1 - 4^-1)-1
= (1/3 + 1/4 ) ^-1
= {(4+3)/12}^-1
=(7/12)^-1
=12/7


9) (1/3)^-3 + (1/2)^-5 - (1/2)^-5
= 3^3 + 2^5 - 2^5
= 3^3
= 27


10) (1/3)^0 = 1 [a^0 = 1]