Solve frac{6^{5^{1^{2}}}*6^{3^{0^{2}}}*((6^{3})^2)^4}{(6^15)^2}

$$\frac { 6 ^ { 5 ^ { 1 ^ { 2 } } } \times 6 ^ { 3 ^ { 0 ^ { 2 } } } \times ( ( 6 ^ { 3 } ) ^ { 2 } ) ^ { 4 } } { ( 6 ^ { 15 } ) ^ { 2 } }$$

Evaluate

$$1$$

Solution Steps

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

$$\frac{6^{5^{1^{2}}}\times 6^{3^{0^{2}}}\times \left(6^{6}\right)^{4}}{\left(6^{15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 4 to get 24.

$$\frac{6^{5^{1^{2}}}\times 6^{3^{0^{2}}}\times 6^{24}}{\left(6^{15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 15 and 2 to get 30.

$$\frac{6^{5^{1^{2}}}\times 6^{3^{0^{2}}}\times 6^{24}}{6^{30}}$$

Cancel out 6^{24} in both numerator and denominator.

$$\frac{6^{3^{0^{2}}}\times 6^{5^{1^{2}}}}{6^{6}}$$

Calculate 0 to the power of 2 and get 0.

$$\frac{6^{3^{0}}\times 6^{5^{1^{2}}}}{6^{6}}$$

Calculate 3 to the power of 0 and get 1.

$$\frac{6^{1}\times 6^{5^{1^{2}}}}{6^{6}}$$

Calculate 6 to the power of 1 and get 6.

$$\frac{6\times 6^{5^{1^{2}}}}{6^{6}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{6\times 6^{5^{1}}}{6^{6}}$$

Calculate 5 to the power of 1 and get 5.

$$\frac{6\times 6^{5}}{6^{6}}$$

Calculate 6 to the power of 5 and get 7776.

$$\frac{6\times 7776}{6^{6}}$$

Multiply 6 and 7776 to get 46656.

$$\frac{46656}{6^{6}}$$

Calculate 6 to the power of 6 and get 46656.

$$\frac{46656}{46656}$$

Divide 46656 by 46656 to get 1.

$$1$$

Factor

$$1$$