Solve frac{(3^{2}*3^5)^0}{(3*3^7)^5}

$$\frac { ( 3 ^ { 2 } \cdot 3 ^ { 5 } ) ^ { 0 } } { ( 3 \cdot 3 ^ { 7 } ) ^ { 5 } }$$

Evaluate

$$\frac{1}{12157665459056928801}\approx 8.22526334 \cdot 10^{-20}$$

Solution Steps

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

$$\frac{\left(3^{7}\right)^{0}}{\left(3\times 3^{7}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 0 to get 0.

$$\frac{3^{0}}{\left(3\times 3^{7}\right)^{5}}$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$\frac{3^{0}}{\left(3^{8}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 5 to get 40.

$$\frac{3^{0}}{3^{40}}$$

Rewrite 3^{40} as 3^{0}\times 3^{40}. Cancel out 3^{0} in both numerator and denominator.

$$\frac{1}{3^{40}}$$

Calculate 3 to the power of 40 and get 12157665459056928801.

$$\frac{1}{12157665459056928801}$$

Factor

$$\frac{1}{3 ^ {40}} = 8.22526333996996 \times 10^{-20}$$