Math, asked by dhillon1284, 11 months ago

the value of (-3/8)^-3 x (4/9)^-2 is _____​

Answers

Answered by mhanifa
24

Answer:

-96

Step-by-step explanation:

(-3/8)^-3 x (4/9)^-2=

-(8/3)^3 x (9/4)^2=

-(2^3/3)^3 x (3^2/2^2)^2=

-2^9/3^3 x 3^4/2^4=

-2^9/2^4 x 3^4/3^3=

-2^5 x 3= -96

Answered by aburaihana123
3

Answer:

The value of   (\frac{- 3}{8} )^{-3} × (\frac{4}{9} )^{-2} is -96

Step-by-step explanation:

Given: The given term is (\frac{- 3}{8} )^{-3} × (\frac{4}{9} )^{-2}

To find: The value of the term  (\frac{- 3}{8} )^{-3} × (\frac{4}{9} )^{-2}

Solution:

The given term is (\frac{- 3}{8} )^{-3} × (\frac{4}{9} )^{-2}

we know that,

The product formula for different power is

(\frac{a}{b} )^{-m}  = (\frac{b}{a} )^{m}

Rewrite the given term according to the formula

(\frac{- 3}{8} )^{-3} =( \frac{8}{-3} )^{3}

(\frac{4}{9} )^{-2}=( \frac{9}{4} )^{2}

Expand the term and write

(\frac{8}{-3} )^{3} *( \frac{9}{4} )^{2} = \frac{8}{-3} ×  \frac{8}{-3} × \frac{8}{-3} × \frac{9}{4} × \frac{9}{4}

On simplifying we get

  (\frac{8}{-3} )^{3} *( \frac{9}{4} )^{2}  = \frac{(8)(2)(2)(3)}{-1}

                     = \frac{96}{-1}

                    = -96

(\frac{8}{-3} )^{3} *( \frac{9}{4} )^{2}  = -96

Final answer:

The value of   (\frac{- 3}{8} )^{-3} × (\frac{4}{9} )^{-2} is -96

#SPJ3

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