Solve frac{(5^{3/2}*2^{7/2})^{2}*3^5/4}{2^15*(3^1/8)^2}

$$\frac { ( 5 ^ { 3 / 2 } \times 2 ^ { 7 / 2 } ) ^ { 2 } \times 3 ^ { 5 / 4 } } { 2 ^ { 15 } \times ( 3 ^ { 1 / 8 } ) ^ { 2 } }$$

Evaluate

$$\frac{375}{256}=1.46484375$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{1}{8} and 2 to get \frac{1}{4}.

$$\frac{\left(5^{\frac{3}{2}}\times 2^{\frac{7}{2}}\right)^{2}\times 3^{\frac{5}{4}}}{2^{15}\times 3^{\frac{1}{4}}}$$

Cancel out \sqrt[4]{3} in both numerator and denominator.

$$\frac{3\times \left(2^{\frac{7}{2}}\times 5^{\frac{3}{2}}\right)^{2}}{2^{15}}$$

Expand \left(2^{\frac{7}{2}}\times 5^{\frac{3}{2}}\right)^{2}.

$$\frac{3\times \left(2^{\frac{7}{2}}\right)^{2}\times \left(5^{\frac{3}{2}}\right)^{2}}{2^{15}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{2} and 2 to get 7.

$$\frac{3\times 2^{7}\times \left(5^{\frac{3}{2}}\right)^{2}}{2^{15}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{2} and 2 to get 3.

$$\frac{3\times 2^{7}\times 5^{3}}{2^{15}}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{3\times 128\times 5^{3}}{2^{15}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{3\times 128\times 125}{2^{15}}$$

Multiply 128 and 125 to get 16000.

$$\frac{3\times 16000}{2^{15}}$$

Multiply 3 and 16000 to get 48000.

$$\frac{48000}{2^{15}}$$

Calculate 2 to the power of 15 and get 32768.

$$\frac{48000}{32768}$$

Reduce the fraction \frac{48000}{32768} to lowest terms by extracting and canceling out 128.

$$\frac{375}{256}$$

Factor

$$\frac{3 \cdot 5 ^ {3}}{2 ^ {8}} = 1\frac{119}{256} = 1.46484375$$