Question

Find the value of x in the equation 4⁵x(2³x)²=256

Answer 1

${4}^{5} \times {( {2}^{3} x)}^{2} = 256 \\ impilies \: {4}^{5} \times {2}^{6} {x}^{2} = 256 \\ implies \: {4}^{5} \times {4}^{3} \times {x}^{2} = 256 \\ implies \: {4}^{8} \times {x}^{2} = 256 \\ implies \: {x}^{2} = 256 \times \frac{1}{ {4}^{8} } \\ implies \: {x}^{2} = {4}^{4} \times \frac{1}{ {4}^{8} } \\ implies \: {x}^{2} = \frac{1}{ {4}^{8} } \\ implies \: x = \sqrt{ \frac{1}{ {4}^{8} } } \\ implies \: x = \frac{1}{256} \\ implies \: x = \frac{1}{ {4}^{4} } \\ implies \: x = {4}^{ - 4}$

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