Solve frac{3^{-5}*3^-2*3^3}{3^8*3^5}

$$\frac { 3 ^ { - 5 } \cdot 3 ^ { - 2 } \cdot 3 ^ { 3 } } { 3 ^ { 8 } \cdot 3 ^ { 5 } }$$

Evaluate

$$\frac{1}{129140163}\approx 7.743524375 \cdot 10^{-9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and -2 to get -7.

$$\frac{3^{-7}\times 3^{3}}{3^{8}\times 3^{5}}$$

To multiply powers of the same base, add their exponents. Add -7 and 3 to get -4.

$$\frac{3^{-4}}{3^{8}\times 3^{5}}$$

To multiply powers of the same base, add their exponents. Add 8 and 5 to get 13.

$$\frac{3^{-4}}{3^{13}}$$

Rewrite 3^{13} as 3^{-4}\times 3^{17}. Cancel out 3^{-4} in both numerator and denominator.

$$\frac{1}{3^{17}}$$

Calculate 3 to the power of 17 and get 129140163.

$$\frac{1}{129140163}$$

Factor

$$\frac{1}{3 ^ {17}} = 7.743524375139591 \times 10^{-9}$$