Solve left(2^5right)^6left(3^3right)^2/{left({2^6right)}^5{left({3}^7right)}^3}

$$\frac{ { \left( { 2 }^{ 5 } \right) }^{ 6 } { \left( { 3 }^{ 3 } \right) }^{ 2 } }{ { \left( { 2 }^{ 6 } \right) }^{ 5 } { \left( { 3 }^{ 7 } \right) }^{ 3 } }$$

Evaluate

$$\frac{1}{14348907}\approx 0.00000007$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 6 to get 30.

$$\frac{2^{30}\times \left(3^{3}\right)^{2}}{\left(2^{6}\right)^{5}\times \left(3^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{30}\times 3^{6}}{\left(2^{6}\right)^{5}\times \left(3^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 5 to get 30.

$$\frac{2^{30}\times 3^{6}}{2^{30}\times \left(3^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{2^{30}\times 3^{6}}{2^{30}\times 3^{21}}$$

Cancel out 2^{30}\times 3^{6} in both numerator and denominator.

$$\frac{1}{3^{15}}$$

Calculate 3 to the power of 15 and get 14348907.

$$\frac{1}{14348907}$$

Factor

$$\frac{1}{3 ^ {15}} = 6.9691719376256325 \times 10^{-8}$$