Solve left(6^26^46^36right)^3div{left({2}^6{3}^6right)}^5

$${ \left( { 6 }^{ 2 } { 6 }^{ 4 } { 6 }^{ 3 } 6 \right) }^{ 3 } \div { \left( { 2 }^{ 6 } { 3 }^{ 6 } \right) }^{ 5 }$$

Evaluate

$$1$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\left(6^{9}\times 6\right)^{3}}{\left(2^{6}\times 3^{6}\right)^{5}}$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\frac{\left(6^{10}\right)^{3}}{\left(2^{6}\times 3^{6}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 3 to get 30.

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

Calculate 6 to the power of 30 and get 221073919720733357899776.

$$\frac{221073919720733357899776}{\left(2^{6}\times 3^{6}\right)^{5}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{221073919720733357899776}{\left(64\times 3^{6}\right)^{5}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{221073919720733357899776}{\left(64\times 729\right)^{5}}$$

Multiply 64 and 729 to get 46656.

$$\frac{221073919720733357899776}{46656^{5}}$$

Calculate 46656 to the power of 5 and get 221073919720733357899776.

$$\frac{221073919720733357899776}{221073919720733357899776}$$

Divide 221073919720733357899776 by 221073919720733357899776 to get 1.

$$1$$

Factor

$$1$$