$${2^{0.2}} \times 64 \times {8^{1.3}} \times {4^{0.2}} = {8^?}$$

Solution

Expression : $${2^{0.2}} \times 64 \times {8^{1.3}} \times {4^{0.2}} = {8^?}$$

=> $$(2)^{0.2} \times (2)^6 \times (2)^{3 \times 1.3} \times (2)^{2 \times 0.2} = (2)^{3 \times x}$$

=> $$(2)^{0.2 + 6 + 3.9 + 0.4} = (2)^{3 x}$$

=> $$(2)^{10.5} = (2)^{3 x}$$

Comparing powers of 2, we get :

=> $$3x = 10.5$$

=> $$x = \frac{10.5}{3} = 3.5$$

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