Solve 5210^3-33^6/49{left(1/2right)}^7

$$\frac{ 52 { 10 }^{ 3 } -3 { 3 }^{ 6 } }{ 4 } 9 { \left( \frac{ 1 }{ 2 } \right) }^{ 7 }$$

Evaluate

$$\frac{448317}{512}=875.619140625$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{52\times 10^{3}-3^{7}}{4}\times 9\times \left(\frac{1}{2}\right)^{7}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{52\times 1000-3^{7}}{4}\times 9\times \left(\frac{1}{2}\right)^{7}$$

Multiply 52 and 1000 to get 52000.

$$\frac{52000-3^{7}}{4}\times 9\times \left(\frac{1}{2}\right)^{7}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{52000-2187}{4}\times 9\times \left(\frac{1}{2}\right)^{7}$$

Subtract 2187 from 52000 to get 49813.

$$\frac{49813}{4}\times 9\times \left(\frac{1}{2}\right)^{7}$$

Express \frac{49813}{4}\times 9 as a single fraction.

$$\frac{49813\times 9}{4}\times \left(\frac{1}{2}\right)^{7}$$

Multiply 49813 and 9 to get 448317.

$$\frac{448317}{4}\times \left(\frac{1}{2}\right)^{7}$$

Calculate \frac{1}{2} to the power of 7 and get \frac{1}{128}.

$$\frac{448317}{4}\times \frac{1}{128}$$

Multiply \frac{448317}{4} times \frac{1}{128} by multiplying numerator times numerator and denominator times denominator.

$$\frac{448317\times 1}{4\times 128}$$

Do the multiplications in the fraction \frac{448317\times 1}{4\times 128}.

$$\frac{448317}{512}$$

Factor

$$\frac{3 ^ {2} \cdot 109 \cdot 457}{2 ^ {9}} = 875\frac{317}{512} = 875.619140625$$