Question

simplify:- (32/243) raise to power -1/5​

Answer 1

Answer:

3/2

Step-by-step explanation:

(32/243)^-1/5=(243/32)^1/5

243=3⁵ 32=2⁵

((3/2)⁵)^1/5

(3/2)¹=3/2

Answer 2

Answer:

$\frac{3}{2}$ is the answer.

Step-by-step explanation:

• Using the property : $(\frac{a}{b} )^{-1} = (\frac{b}{a} )^{1}$

                        $(\frac{32}{243} )^{\frac{-1}{5} }$$= (\frac{243}{32} )^{\frac{1}{5} }$

• Using the property :

        $(2)^{5} = 2*2*2*2*2= 32$  and  $(3)^{5} = 3*3*3*3*3 = 243$                                

                            $(\frac{243}{32} )^{\frac{1}{5} }$  $= (\frac{3^{5} }{2^{5} } )^{\frac{1}{5} }$

• Using the property: $(a^{m}) ^{n} = (a)^{m*n}$

                          $(\frac{3^{5} }{2^{5} } )^{\frac{1}{5} } =( (\frac{3}{2} )^{5} )^{\frac{1}{5} }$

                          $(\frac{3}{2} ^{5} )^{\frac{1}{5} } =$  $(\frac{3}{2} )^{1} = \frac{3}{2}$

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