Question

find the value of 64 by 25 hole to the power of minus 3 by 2​

Answer 1

Step-by-step explanation:

(64/25)^-3/2=(25/64)^3/2=(5/8)^2*3/2=(5/8)³=125/512.

Answer 2

The value = $\frac{125}{512}$

GIVEN:- 64 by 25 whole to the power of minus 3 by 2

TO FIND:- the value

SOLUTION:-

• Power implies exponents where say, a by b whole to the power 2 = (a/b)²

according to the question, 64 by 25 whole to the power of minus 3 by 2 means

$( { \frac{64}{25} )}^{ - \frac{3}{2} }$

64 can be written as (8 × 8) = 8²

25 can be written as (5 × 5) = 5²

Now putting these values

$( { \frac{ {8}^{2} }{ {5}^{2} } })^{ - \frac{3}{2} }$

As we know,

$( { {a}^{m} })^{n} = {a}^{m \times n}$

Similarly,

$= \frac{ {8}^{2 \times - \frac{3}{2} } }{ {5}^{2 \times - \frac{3}{2} } } \\ = \frac{ {8}^{ - 3} }{ {5}^{ - 3} } \\ = \frac{1}{ {8}^{3} } \times {5}^{3} \\ = \frac{ {5}^{3} }{ {8}^{3} } \\ = \frac{125}{512}$

Hence, the value is $\frac{125}{512}$

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