If a and b are distinct positive primes such that -a6b-4-ax b2 y-find x and y-

√(a^6b^ 4)=a^x b^2 y (a^6b^ 4)^1/3=a^x b^2 y a^6/3.b^ 4/3=a^x b^2 y⇒ a^2.b^ 4/3=a^x .b^2 y Comparing,we get a^x=a^2⇒ x=2 and b^ 4/3=b^2 y⇒ 2y= 4/3 ⇒ y= 4/3×2= 2 ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

If a and b ar...

Question

If a and b are distinct positive primes such that $\sqrt[3]{a^{6} b^{- 4}} = a^{x} b^{2 y}$ ,find x and y.

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Solution

$\sqrt[3]{a^{6} b^{- 4}} = a^{x} b^{2 y} (a^{6} b^{- 4})^{\frac{1}{3}} = a^{x} b^{2 y} a^{\frac{6}{3}} . b^{\frac{- 4}{3}} = a^{x} b^{2 y} \Rightarrow a^{2} . b^{\frac{- 4}{3}} = a^{x} . b^{2 y} C o m p a r i n g, w e g e t a^{x} = a^{2} \Rightarrow x = 2 a n d b^{\frac{- 4}{3}} = b^{2 y} \Rightarrow 2 y = \frac{- 4}{3} \Rightarrow y = \frac{- 4}{3 \times 2} = \frac{- 2}{3} ∴ x = 2, y = \frac{- 2}{3}$

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If a and b are distinct positive primes such that 3√a6b−4=axb2y,find x and y.

3√a6b−4=axb2y(a6b−4)13=axb2ya63.b−43=axb2y⇒a2.b−43=ax.b2yComparing,we getax=a2⇒x=2and b−43=b2y⇒2y=−43⇒y=−43×2=−23∴x=2,y=−23

If a and b are distinct positive primes such that $\sqrt[3]{a^{6} b^{- 4}} = a^{x} b^{2 y}$ ,find x and y.