$$(0.8)^{2.5}\times\frac{(0.8)^{1.5}}{(0.8)^{0.5}}=(0.2)^{3.5}\times2^{?}$$

Solution

Expression : $$(0.8)^{2.5}\times\frac{(0.8)^{1.5}}{(0.8)^{0.5}}=(0.2)^{3.5}\times2^{?}$$

=> $$(0.8)^{2.5 + 1.5 - 0.5} = (0.2)^{3.5} \times 2^{x}$$

=> $$(0.8)^{3.5} = (0.2)^{3.5} \times 2^{x}$$

=> $$2^x = \frac{(0.8)^{3.5}}{(0.2)^{3.5}}$$

=> $$2^x = (4)^{3.5} = 2^7$$

=> $$x = 7$$

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