Solve left(8^2right)^left(2^2right)^2/20/40/100

$$\frac{ \frac{ \frac{ { \left( { 8 }^{ 2 } \right) }^{ { \left( { 2 }^{ 2 } \right) }^{ 2 } } }{ 20 } }{ 40 } }{ 100 }$$

Evaluate

$$\frac{618970019642690137449562112}{625}=9.903520314 \cdot 10^{23}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\frac{\frac{\left(8^{2}\right)^{2^{4}}}{20}}{40}}{100}$$

Express \frac{\frac{\frac{\left(8^{2}\right)^{2^{4}}}{20}}{40}}{100} as a single fraction.

$$\frac{\frac{\left(8^{2}\right)^{2^{4}}}{20}}{40\times 100}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\frac{64^{2^{4}}}{20}}{40\times 100}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\frac{64^{16}}{20}}{40\times 100}$$

Calculate 64 to the power of 16 and get 79228162514264337593543950336.

$$\frac{\frac{79228162514264337593543950336}{20}}{40\times 100}$$

Reduce the fraction \frac{79228162514264337593543950336}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{19807040628566084398385987584}{5}}{40\times 100}$$

Multiply 40 and 100 to get 4000.

$$\frac{\frac{19807040628566084398385987584}{5}}{4000}$$

Express \frac{\frac{19807040628566084398385987584}{5}}{4000} as a single fraction.

$$\frac{19807040628566084398385987584}{5\times 4000}$$

Multiply 5 and 4000 to get 20000.

$$\frac{19807040628566084398385987584}{20000}$$

Reduce the fraction \frac{19807040628566084398385987584}{20000} to lowest terms by extracting and canceling out 32.

$$\frac{618970019642690137449562112}{625}$$

Factor

$$\frac{2 ^ {89}}{5 ^ {4}} = 9.903520314283043 \times 10^{23}\frac{237}{625} = 9.903520314283043 \times 10^{23}$$