Solve 3^-10+3^12/3^10+3^-12

$$\frac{ { 3 }^{ -10 } + { 3 }^{ 12 } }{ { 3 }^{ 10 } + { 3 }^{ -12 } }$$

Evaluate

$$9$$

Solution Steps

Calculate 3 to the power of -10 and get \frac{1}{59049}.

$$\frac{\frac{1}{59049}+3^{12}}{3^{10}+3^{-12}}$$

Calculate 3 to the power of 12 and get 531441.

$$\frac{\frac{1}{59049}+531441}{3^{10}+3^{-12}}$$

Add \frac{1}{59049} and 531441 to get \frac{31381059610}{59049}.

$$\frac{\frac{31381059610}{59049}}{3^{10}+3^{-12}}$$

Calculate 3 to the power of 10 and get 59049.

$$\frac{\frac{31381059610}{59049}}{59049+3^{-12}}$$

Calculate 3 to the power of -12 and get \frac{1}{531441}.

$$\frac{\frac{31381059610}{59049}}{59049+\frac{1}{531441}}$$

Add 59049 and \frac{1}{531441} to get \frac{31381059610}{531441}.

$$\frac{\frac{31381059610}{59049}}{\frac{31381059610}{531441}}$$

Divide \frac{31381059610}{59049} by \frac{31381059610}{531441} by multiplying \frac{31381059610}{59049} by the reciprocal of \frac{31381059610}{531441}.

$$\frac{31381059610}{59049}\times \frac{531441}{31381059610}$$

Multiply \frac{31381059610}{59049} and \frac{531441}{31381059610} to get 9.

$$9$$

Factor

$$3^{2}$$