Solve 5*3^{3}(2*1^{-1}*2^4*3)*(1/2*1^5*2^4*3^-3)

$$5 \cdot 3 ^ { 3 } ( 2 \cdot 1 ^ { - 1 } \cdot 2 ^ { 4 } \cdot 3 ) \cdot ( \frac { 1 } { 2 } \cdot 1 ^ { 5 } \cdot 2 ^ { 4 } \cdot 3 ^ { - 3 } )$$

Evaluate

$$3840$$

Solution Steps

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

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

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

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

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

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

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

$$5\times 3^{1}\times 2^{9}\times 1^{-1}\times \frac{1}{2}\times 1^{5}$$

To multiply powers of the same base, add their exponents. Add -1 and 5 to get 4.

$$5\times 3^{1}\times 2^{9}\times 1^{4}\times \frac{1}{2}$$

Calculate 3 to the power of 1 and get 3.

$$5\times 3\times 2^{9}\times 1^{4}\times \frac{1}{2}$$

Multiply 5 and 3 to get 15.

$$15\times 2^{9}\times 1^{4}\times \frac{1}{2}$$

Calculate 2 to the power of 9 and get 512.

$$15\times 512\times 1^{4}\times \frac{1}{2}$$

Multiply 15 and 512 to get 7680.

$$7680\times 1^{4}\times \frac{1}{2}$$

Calculate 1 to the power of 4 and get 1.

$$7680\times 1\times \frac{1}{2}$$

Multiply 7680 and 1 to get 7680.

$$7680\times \frac{1}{2}$$

Multiply 7680 and \frac{1}{2} to get 3840.

$$3840$$

Factor

$$2^{8}\times 3\times 5$$