Solve 5+[(5^{2}*5^{3}*5)^{2}]^3:(5^4*5^2*5)^5

$$5 + [ ( 5 ^ { 2 } \cdot 5 ^ { 3 } \cdot 5 ) ^ { 2 } ] ^ { 3 } : ( 5 ^ { 4 } \cdot 5 ^ { 2 } \cdot 5 ) ^ { 5 }$$

Evaluate

$$10$$

Solution Steps

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

$$5+\frac{\left(\left(5^{5}\times 5\right)^{2}\right)^{3}}{\left(5^{4}\times 5^{2}\times 5\right)^{5}}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$5+\frac{\left(5^{12}\right)^{3}}{\left(5^{4}\times 5^{2}\times 5\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 3 to get 36.

$$5+\frac{5^{36}}{\left(5^{4}\times 5^{2}\times 5\right)^{5}}$$

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

$$5+\frac{5^{36}}{\left(5^{6}\times 5\right)^{5}}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$5+\frac{5^{36}}{\left(5^{7}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 5 to get 35.

$$5+\frac{5^{36}}{5^{35}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 35 from 36 to get 1.

$$5+5^{1}$$

Calculate 5 to the power of 1 and get 5.

$$5+5$$

Add 5 and 5 to get 10.

$$10$$

Factor

$$2\times 5$$