Question

please help I need to do this please ASAP

Answer 1

Step-by-step explanation:

Given :-

(32/243)⅗ ÷[(25/9)³/² ×(5/2)-³] +4/(216)-⅔

To find :-

Simplify the expression ?

Solution :-

Given expression is

(32/243)⅗ ÷ [(25/9)³/² ×(5/2)-³] +4/(216)-⅔

32 = 2×2×2×2×2 = 2⁵

243 = 3×3×3×3×3 = 3⁵

32/243 = 2⁵/3⁵ = (2/3)⁵

25 = 5×5 = 5²

9 = 3×3 = 3²

25/9 = 5²/3² = (5/3)²

216 = 6×6×6 = 6³

Now above expression becomes

=> [(2/3)⁵]⅗ ÷ [( (5/3)²)³/² ×(5/2)-³] + 4/(6³)-⅔

We know that (a^m)^n = a^(mn)

=> (2/3)³ ÷ [(5/3)³× (5/2)-³] + (4/6-²)

=> (2/3)³ ÷[(5/3)³×(2/5/³] +4/(1/6²)

Since a^-n = 1/a^n

=> (2/3)³ ÷[(5/3)³×(2/5/³] +4/(1/6²)

=> (2/3)³÷ [ (5³×2³)/(3³×5³)] +(4×6²)

Since (ab)^m = a^m × b^m

=> (2/3)³÷(2³/3³)+(4×36)

=> (2³/3³)×(3³/2³)+(144)

=> (2³×3³)/(3³×2³)+144

=>1+144

=> 145

Answer:-

The value of the given expresion is 145

Used formulae:-

• (a^m)^n = a^(mn)
• a^-n = 1/a^n
• (ab)^m = a^m × b^m
• (a/b)^m = a^m / b^m

Answer 2

Answer:

36/16

Step-by-step explanation:

Your answer is 36/16