Solve left(3^23^5right)^6/{left(33^7right)^5}

$$\frac{ { \left( { 3 }^{ 2 } { 3 }^{ 5 } \right) }^{ 6 } }{ { \left(3 { 3 }^{ 7 } \right) }^{ 5 } }$$

Evaluate

$$9$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\left(3^{7}\right)^{6}}{\left(3\times 3^{7}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 6 to get 42.

$$\frac{3^{42}}{\left(3\times 3^{7}\right)^{5}}$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$\frac{3^{42}}{\left(3^{8}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 5 to get 40.

$$\frac{3^{42}}{3^{40}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 40 from 42 to get 2.

$$3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9$$

Factor

$$3^{2}$$