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Can someone help me find the equivalent expressions to the picture below? I’m having trouble

Can someone help me find the equivalent expressions to the picture below? I’m having-example-1
User Mollymerp
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1 Answer

5 votes

Answer:

Options (1), (2), (3) and (7)

Explanation:

Given expression is
\frac{\sqrt[3]{8^{(1)/(3)}* 3} }{3*2^{(1)/(9)}}.

Now we will solve this expression with the help of law of exponents.


\frac{\sqrt[3]{8^{(1)/(3)}* 3} }{3*2^{(1)/(9)}}=\frac{\sqrt[3]{(2^3)^{(1)/(3)}* 3} }{3*2^{(1)/(9)}}


=\frac{\sqrt[3]{2* 3} }{3*2^{(1)/(9)}}


=\frac{2^{(1)/(3)}* 3^{(1)/(3)}}{3* 2^{(1)/(9)}}


=2^{(1)/(3)}* 3^{(1)/(3)}* 2^{-(1)/(9)}* 3^(-1)


=2^{(1)/(3)-(1)/(9)}* 3^{(1)/(3)-1}


=2^{(3-1)/(9)}* 3^{(1-3)/(3)}


=2^{(2)/(9)}* 3^{-(2)/(3) } [Option 2]


2^{(2)/(9)}* 3^{-(2)/(3) }=(\sqrt[9]{2})^2* (\sqrt[3]{(1)/(3) } )^2 [Option 1]


2^{(2)/(9)}* 3^{-(2)/(3) }=(\sqrt[9]{2})^2* (\sqrt[3]{(1)/(3) } )^2


=(2^2)^{(1)/(9)}* (3^2)^{-(1)/(3) }


=\sqrt[9]{4}* \sqrt[3]{(1)/(9) } [Option 3]


2^{(2)/(9)}* 3^{-(2)/(3) }=(2^2)^{(1)/(9)}* (3^(-2))^{(1)/(3) }


=\sqrt[9]{2^2}* \sqrt[3]{3^(-2)} [Option 7]

Therefore, Options (1), (2), (3) and (7) are the correct options.

User Pheobe
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