Solve 9^21/27^10H9^20/27^9paBHO

$$\frac { 9 ^ { 21 } } { 27 ^ { 10 } } H \frac { 9 ^ { 20 } } { 27 ^ { 9 } } paBHO$$

Evaluate

$$847288609443BOapH^{2}$$

Solution Steps

Multiply H and H to get H^{2}.

$$\frac{9^{21}}{27^{10}}H^{2}\times \frac{9^{20}}{27^{9}}paBO$$

Calculate 9 to the power of 21 and get 109418989131512359209.

$$\frac{109418989131512359209}{27^{10}}H^{2}\times \frac{9^{20}}{27^{9}}paBO$$

Calculate 27 to the power of 10 and get 205891132094649.

$$\frac{109418989131512359209}{205891132094649}H^{2}\times \frac{9^{20}}{27^{9}}paBO$$

Divide 109418989131512359209 by 205891132094649 to get 531441.

$$531441H^{2}\times \frac{9^{20}}{27^{9}}paBO$$

Calculate 9 to the power of 20 and get 12157665459056928801.

$$531441H^{2}\times \frac{12157665459056928801}{27^{9}}paBO$$

Calculate 27 to the power of 9 and get 7625597484987.

$$531441H^{2}\times \frac{12157665459056928801}{7625597484987}paBO$$

Divide 12157665459056928801 by 7625597484987 to get 1594323.

$$531441H^{2}\times 1594323paBO$$

Multiply 531441 and 1594323 to get 847288609443.

$$847288609443H^{2}paBO$$

Differentiate w.r.t. p

$$847288609443BOaH^{2}$$