Solve [(13^{8}*13^3):13^13:13^6]*13^2

$$[ ( 13 ^ { 8 } \cdot 13 ^ { 3 } ) : 13 ^ { 13 } : 13 ^ { 6 } ] \cdot 13 ^ { 2 }$$

Evaluate

$$\frac{1}{4826809}\approx 0.000000207$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$\frac{\frac{13^{11}}{13^{13}}}{13^{6}}\times 13^{2}$$

Rewrite 13^{13} as 13^{11}\times 13^{2}. Cancel out 13^{11} in both numerator and denominator.

$$\frac{\frac{1}{13^{2}}}{13^{6}}\times 13^{2}$$

Calculate 13 to the power of 2 and get 169.

$$\frac{\frac{1}{169}}{13^{6}}\times 13^{2}$$

Calculate 13 to the power of 6 and get 4826809.

$$\frac{\frac{1}{169}}{4826809}\times 13^{2}$$

Express \frac{\frac{1}{169}}{4826809} as a single fraction.

$$\frac{1}{169\times 4826809}\times 13^{2}$$

Multiply 169 and 4826809 to get 815730721.

$$\frac{1}{815730721}\times 13^{2}$$

Calculate 13 to the power of 2 and get 169.

$$\frac{1}{815730721}\times 169$$

Multiply \frac{1}{815730721} and 169 to get \frac{169}{815730721}.

$$\frac{169}{815730721}$$

Reduce the fraction \frac{169}{815730721} to lowest terms by extracting and canceling out 169.

$$\frac{1}{4826809}$$

Factor

$$\frac{1}{13 ^ {6}} = 2.0717621103300337 \times 10^{-7}$$