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Exponents with Like Bases

If a= b2x, ...

Question

If $a = b^{2 x}, b = c^{2 y}$ & $c = a^{2 z}$ , prove that xyz= $\frac{1}{8}$

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Solution

$a = b^{2 x} a = (c^{2 y})^{2 x} o r a = c^{4 x y} o r a = (a^{2 z})^{4 x y} o r a = a^{8 x y z} ∴ 8 x y z = 1 ∴ x y z = (\frac{1}{8})$

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