If a and b are distinct primes such that a 6 b-43-a x b 2 y- find x and y-

Given: a6b 43=axb2y a6b 43=axb2y #8658;a6b 413=axb2y #8658;a6 #215;13b 4 #215;13=axb2y #8658;a2b 43=axb2y #8658;x=2 #160; #160;and #160;y= 23 ...

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Question

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

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Solution

Given: $\sqrt[3]{a^{6} b^{- 4}} = a^{x} b^{2 y}$
$\sqrt[3]{a^{6} b^{- 4}} = a^{x} b^{2 y} \Rightarrow {(a^{6} b^{- 4})}^{\frac{1}{3}} = a^{x} b^{2 y} \Rightarrow a^{6 \times \frac{1}{3}} b^{- 4 \times \frac{1}{3}} = a^{x} b^{2 y} \Rightarrow a^{2} b^{- \frac{4}{3}} = a^{x} b^{2 y} \Rightarrow x = 2 and y = - \frac{2}{3}$

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If a and b are distinct primes such that a6b-43=axb2y, find x and y.

Given: a6b-43=axb2y a6b-43=axb2y⇒a6b-413=axb2y⇒a6×13b-4×13=axb2y⇒a2b-43=axb2y⇒x=2 and y=-23

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