Question

SIMPLIFY
( 1\frac{61}{64}) ^{-2/3}

Answer 1

After simplification, we get 247.9

Step-by-step explanation:

We are given that

= 1/ (64*61)^-2/3

After solving the brackets

= 1/ 3904^-2/3

Since, we know that when we reciprocate a value, the sign of its power changes. Therefore,

=  3904^2/3

Now, solving the power, we get

= 247.9

Answer 2

$( 1\frac{61}{64}) ^{-2/3}$   = 0.64  

Step-by-step explanation:

$( 1\frac{61}{64}) ^{-2/3}$

$1\frac{61}{64} = \frac{64 \times 1 + 61}{64} = \frac{125}{64}$  

125/64  = 5³/4³  = (5/4)³

=> $( 1\frac{61}{64}) ^{-2/3}$   =  $((5/4)^3)^{\frac{-2}{3}}$

= (5/4)⁻²

=  (4/5)²

=  4²/5²

= 16/25

= 16 * 4 / 25 * 4

= 64/100

= 0.64

$( 1\frac{61}{64}) ^{-2/3}$   = 0.64  

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