Solve (3^{-1}+3^-2+3^-3)^-2*(13)^2

$$( 3 ^ { - 1 } + 3 ^ { - 2 } + 3 ^ { - 3 } ) ^ { - 2 } \cdot ( 13 ) ^ { 2 }$$

Evaluate

$$729$$

Solution Steps

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

$$\left(\frac{1}{3}+3^{-2}+3^{-3}\right)^{-2}\times 13^{2}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\left(\frac{1}{3}+\frac{1}{9}+3^{-3}\right)^{-2}\times 13^{2}$$

Add \frac{1}{3} and \frac{1}{9} to get \frac{4}{9}.

$$\left(\frac{4}{9}+3^{-3}\right)^{-2}\times 13^{2}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\left(\frac{4}{9}+\frac{1}{27}\right)^{-2}\times 13^{2}$$

Add \frac{4}{9} and \frac{1}{27} to get \frac{13}{27}.

$$\left(\frac{13}{27}\right)^{-2}\times 13^{2}$$

Calculate \frac{13}{27} to the power of -2 and get \frac{729}{169}.

$$\frac{729}{169}\times 13^{2}$$

Calculate 13 to the power of 2 and get 169.

$$\frac{729}{169}\times 169$$

Multiply \frac{729}{169} and 169 to get 729.

$$729$$

Factor

$$3^{6}$$