Solve [5^{16}:5^{11}:5^{5}+(30^{3}:30:6^2)]:13+(4^4:4^3+4^0)

$$[ 5 ^ { 16 } : 5 ^ { 11 } : 5 ^ { 5 } + ( 30 ^ { 3 } : 30 : 6 ^ { 2 } ) ] : 13 + ( 4 ^ { 4 } : 4 ^ { 3 } + 4 ^ { 0 } )$$

Evaluate

$$7$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 11 from 16 to get 5.

$$\frac{\frac{5^{5}}{5^{5}}+\frac{\frac{30^{3}}{30}}{6^{2}}}{13}+\frac{4^{4}}{4^{3}}+4^{0}$$

Divide 5^{5} by 5^{5} to get 1.

$$\frac{1+\frac{\frac{30^{3}}{30}}{6^{2}}}{13}+\frac{4^{4}}{4^{3}}+4^{0}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$\frac{1+\frac{30^{2}}{6^{2}}}{13}+\frac{4^{4}}{4^{3}}+4^{0}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 4 to get 1.

$$\frac{1+\frac{30^{2}}{6^{2}}}{13}+4^{1}+4^{0}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{1+\frac{900}{6^{2}}}{13}+4^{1}+4^{0}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{1+\frac{900}{36}}{13}+4^{1}+4^{0}$$

Divide 900 by 36 to get 25.

$$\frac{1+25}{13}+4^{1}+4^{0}$$

Add 1 and 25 to get 26.

$$\frac{26}{13}+4^{1}+4^{0}$$

Divide 26 by 13 to get 2.

$$2+4^{1}+4^{0}$$

Calculate 4 to the power of 1 and get 4.

$$2+4+4^{0}$$

Add 2 and 4 to get 6.

$$6+4^{0}$$

Calculate 4 to the power of 0 and get 1.

$$6+1$$

Add 6 and 1 to get 7.

$$7$$

Factor

$$7$$