Solve 3^4+3(3^3)/2-3^2+1

$${ 3 }^{ 4 } + \frac{ 3( { 3 }^{ 3 } ) }{ 2 } - { 3 }^{ 2 } +1$$

Evaluate

$$\frac{227}{2}=113.5$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$3^{4}+\frac{3^{4}}{2}-3^{2}+1$$

Calculate 3 to the power of 4 and get 81.

$$81+\frac{3^{4}}{2}-3^{2}+1$$

Calculate 3 to the power of 4 and get 81.

$$81+\frac{81}{2}-3^{2}+1$$

Convert 81 to fraction \frac{162}{2}.

$$\frac{162}{2}+\frac{81}{2}-3^{2}+1$$

Since \frac{162}{2} and \frac{81}{2} have the same denominator, add them by adding their numerators.

$$\frac{162+81}{2}-3^{2}+1$$

Add 162 and 81 to get 243.

$$\frac{243}{2}-3^{2}+1$$

Calculate 3 to the power of 2 and get 9.

$$\frac{243}{2}-9+1$$

Convert 9 to fraction \frac{18}{2}.

$$\frac{243}{2}-\frac{18}{2}+1$$

Since \frac{243}{2} and \frac{18}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{243-18}{2}+1$$

Subtract 18 from 243 to get 225.

$$\frac{225}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{225}{2}+\frac{2}{2}$$

Since \frac{225}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{225+2}{2}$$

Add 225 and 2 to get 227.

$$\frac{227}{2}$$

Factor

$$\frac{227}{2} = 113\frac{1}{2} = 113.5$$