Solve f=[3/7*(3/7)^2*(3/7)^3]^4:(3/7)^22

$$f = [ \frac { 3 } { 7 } \cdot ( \frac { 3 } { 7 } ) ^ { 2 } \cdot ( \frac { 3 } { 7 } ) ^ { 3 } ] ^ { 4 } : ( \frac { 3 } { 7 } ) ^ { 22 }$$

Solve for f

$$f=\frac{9}{49}\approx 0.183673469$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$f=\frac{\left(\left(\frac{3}{7}\right)^{3}\times \left(\frac{3}{7}\right)^{3}\right)^{4}}{\left(\frac{3}{7}\right)^{22}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$f=\frac{\left(\left(\frac{3}{7}\right)^{6}\right)^{4}}{\left(\frac{3}{7}\right)^{22}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 4 to get 24.

$$f=\frac{\left(\frac{3}{7}\right)^{24}}{\left(\frac{3}{7}\right)^{22}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 22 from 24 to get 2.

$$f=\left(\frac{3}{7}\right)^{2}$$

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$f=\frac{9}{49}$$

Assign f

$$f≔\frac{9}{49}$$