Solve {left({left(7/2right)}^2div7^2right)}^2*x={left({left(1/2right)}^0-5*0.3^2*0.5^-1right)}^2

$${ \left( { \left( \frac{ 7 }{ 2 } \right) }^{ 2 } \div { 7 }^{ 2 } \right) }^{ 2 } \times x= { \left( { \left( \frac{ 1 }{ 2 } \right) }^{ 0 } -5 \times { 0.3 }^{ 2 } \times { 0.5 }^{ -1 } \right) }^{ 2 }$$

Solve for x

$$x=0.16$$

Steps for Solving Linear Equation

Calculate \frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$\left(\frac{\frac{49}{4}}{7^{2}}\right)^{2}x=\left(\left(\frac{1}{2}\right)^{0}-5\times 0.3^{2}\times 0.5^{-1}\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$\left(\frac{\frac{49}{4}}{49}\right)^{2}x=\left(\left(\frac{1}{2}\right)^{0}-5\times 0.3^{2}\times 0.5^{-1}\right)^{2}$$

Express \frac{\frac{49}{4}}{49} as a single fraction.

$$\left(\frac{49}{4\times 49}\right)^{2}x=\left(\left(\frac{1}{2}\right)^{0}-5\times 0.3^{2}\times 0.5^{-1}\right)^{2}$$

Cancel out 49 in both numerator and denominator.

$$\left(\frac{1}{4}\right)^{2}x=\left(\left(\frac{1}{2}\right)^{0}-5\times 0.3^{2}\times 0.5^{-1}\right)^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1}{16}x=\left(\left(\frac{1}{2}\right)^{0}-5\times 0.3^{2}\times 0.5^{-1}\right)^{2}$$

Calculate \frac{1}{2} to the power of 0 and get 1.

$$\frac{1}{16}x=\left(1-5\times 0.3^{2}\times 0.5^{-1}\right)^{2}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$\frac{1}{16}x=\left(1-5\times 0.09\times 0.5^{-1}\right)^{2}$$

Multiply 5 and 0.09 to get 0.45.

$$\frac{1}{16}x=\left(1-0.45\times 0.5^{-1}\right)^{2}$$

Calculate 0.5 to the power of -1 and get 2.

$$\frac{1}{16}x=\left(1-0.45\times 2\right)^{2}$$

Multiply 0.45 and 2 to get 0.9.

$$\frac{1}{16}x=\left(1-0.9\right)^{2}$$

Subtract 0.9 from 1 to get 0.1.

$$\frac{1}{16}x=0.1^{2}$$

Calculate 0.1 to the power of 2 and get 0.01.

$$\frac{1}{16}x=0.01$$

Multiply both sides by 16, the reciprocal of \frac{1}{16}.

$$x=0.01\times 16$$

Multiply 0.01 and 16 to get 0.16.

$$x=0.16$$