Solve [(3^2)^3]div(3)^2(3)^5+3/2div1/3-(2)=

$$[ ( 3 ^ { 2 } ) ^ { 3 } ] \div ( 3 ) ^ { 2 } ( 3 ) ^ { 5 } + \frac { 3 } { 2 } \div \frac { 1 } { 3 } - ( 2 ) =$$

Evaluate

$$\frac{39371}{2}=19685.5$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{3^{6}}{3^{2}}\times 3^{5}+\frac{\frac{3}{2}}{\frac{1}{3}}-2$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 6 to get 4.

$$3^{4}\times 3^{5}+\frac{\frac{3}{2}}{\frac{1}{3}}-2$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$3^{9}+\frac{\frac{3}{2}}{\frac{1}{3}}-2$$

Calculate 3 to the power of 9 and get 19683.

$$19683+\frac{\frac{3}{2}}{\frac{1}{3}}-2$$

Divide \frac{3}{2} by \frac{1}{3} by multiplying \frac{3}{2} by the reciprocal of \frac{1}{3}.

$$19683+\frac{3}{2}\times 3-2$$

Multiply \frac{3}{2} and 3 to get \frac{9}{2}.

$$19683+\frac{9}{2}-2$$

Add 19683 and \frac{9}{2} to get \frac{39375}{2}.

$$\frac{39375}{2}-2$$

Subtract 2 from \frac{39375}{2} to get \frac{39371}{2}.

$$\frac{39371}{2}$$

Factor

$$\frac{39371}{2} = 19685\frac{1}{2} = 19685.5$$