Solve =(3^frac{3{2}}*4*2^-3)(3^frac{1{2}}*4^-frac{1{2}}*2)

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

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 1 and -\frac{1}{2} to get \frac{1}{2}.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Calculate 4 to the power of \frac{1}{2} and get 2.

$$9\times 2\times 2^{-2}$$

Multiply 9 and 2 to get 18.

$$18\times 2^{-2}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$18\times \frac{1}{4}$$

Multiply 18 and \frac{1}{4} to get \frac{9}{2}.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$