Question

Find the value of (4/9)½×64⅔×(1⅓)-¹ ?​

Answer 1

Explanation:

Given :-

(4/9)½×64⅔×(1⅓)-¹

To find :-

Simplify the expression ?

Solution :-

Given expression is

(4/9)½×64⅔×(1⅓)-¹

=> (4/9)½ × (64)⅔ × (4/3)-¹

=> [ (2²/3²)]½ × (4³)⅔ × (4/3)-¹

=> [(2/3)²]½ × (4)³×⅔ × (4/3)-¹

We know that

(a^m )^n = a^(mn)

=> (2/3)²/² × 4⁶/³ × (4/3)-¹

=> (2/3)×4² × (4/3)-¹

=> (2/3)×16×(3/4)

Since a^-n = 1/a^n

=> (2×16×3)/(4×3)

=> 2×4

=> 8

Answer:-

The answer for the given problem is 8

Used formulae:-

→ (a^m )^n = a^(mn)

→ a^-n = 1/a^n

→ (a/b)^m = a^m / a^n