Solve (2^{3}*2^{2})^{3}:(2^{9}*2)-[(3^3)^2]^2:3^15

$$( 2 ^ { 3 } \times 2 ^ { 2 } ) ^ { 3 } : ( 2 ^ { 9 } \times 2 ) - [ ( 3 ^ { 3 } ) ^ { 2 } ] ^ { 2 } : 3 ^ { 15 }$$

Evaluate

$$\frac{863}{27}\approx 31.962962963$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\left(2^{5}\right)^{3}}{2^{9}\times 2}-\frac{\left(\left(3^{3}\right)^{2}\right)^{2}}{3^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{2^{15}}{2^{9}\times 2}-\frac{\left(\left(3^{3}\right)^{2}\right)^{2}}{3^{15}}$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\frac{2^{15}}{2^{10}}-\frac{\left(\left(3^{3}\right)^{2}\right)^{2}}{3^{15}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 15 to get 5.

$$2^{5}-\frac{\left(\left(3^{3}\right)^{2}\right)^{2}}{3^{15}}$$

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

$$2^{5}-\frac{\left(3^{6}\right)^{2}}{3^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$2^{5}-\frac{3^{12}}{3^{15}}$$

Rewrite 3^{15} as 3^{12}\times 3^{3}. Cancel out 3^{12} in both numerator and denominator.

$$2^{5}-\frac{1}{3^{3}}$$

Calculate 2 to the power of 5 and get 32.

$$32-\frac{1}{3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$32-\frac{1}{27}$$

Subtract \frac{1}{27} from 32 to get \frac{863}{27}.

$$\frac{863}{27}$$

Factor

$$\frac{863}{3 ^ {3}} = 31\frac{26}{27} = 31.962962962962962$$