Solve [13^{6}*(13^{5}:13)]^{2}:[13^{13}:(13^2*13^3)^2]^2

$$[ 13 ^ { 6 } \cdot ( 13 ^ { 5 } : 13 ) ] ^ { 2 } : [ 13 ^ { 13 } : ( 13 ^ { 2 } \cdot 13 ^ { 3 } ) ^ { 2 } ] ^ { 2 }$$

Evaluate

$$3937376385699289$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 5 to get 4.

$$\frac{\left(13^{6}\times 13^{4}\right)^{2}}{\left(\frac{13^{13}}{\left(13^{2}\times 13^{3}\right)^{2}}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{\left(13^{10}\right)^{2}}{\left(\frac{13^{13}}{\left(13^{2}\times 13^{3}\right)^{2}}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 2 to get 20.

$$\frac{13^{20}}{\left(\frac{13^{13}}{\left(13^{2}\times 13^{3}\right)^{2}}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{13^{20}}{\left(\frac{13^{13}}{\left(13^{5}\right)^{2}}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{13^{20}}{\left(\frac{13^{13}}{13^{10}}\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 13 to get 3.

$$\frac{13^{20}}{\left(13^{3}\right)^{2}}$$

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

$$\frac{13^{20}}{13^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 20 to get 14.

$$13^{14}$$

Calculate 13 to the power of 14 and get 3937376385699289.

$$3937376385699289$$

Factor

$$13^{14}$$