Question

the value of 64^-3/2 ​

Answer 1

Answer:

64^[-3/2]

= (1/64)^[3/2]

= {(1/8)²}^[3/2]

= (1/8)^[2 × 3/2]

= (1/8)^3

= 1/512

Answer 2

$\frac{1}{512}$

$64^{\frac{-3}{2} }$  ( reciprocal the base to make the power positive )

$(\frac{1}{64} )^{\frac{3}{2} }$ ( Take L.C.M of 64 = $2^{6}$)

$(\frac{1}{2^{6} }) ^{\frac{3}{2} }$        $[1^{\frac{3}{2} } = 1 \\ (2^{6} )^{\frac{3}{2} } = (2^{3)3 } = 2^{9}]$  

On using the laws of exponents $(\frac{x}{y}) ^{m} = \frac{x^{m} }{y^{m} } \\and (x^{m)^{n} } = x^{mn}$

$(\frac{1}{2^{6} }) ^{\frac{3}{2} } = \frac{1}{2^{9} } = \frac{1}{512}$