Solve frac{(3^{2})^5*3^3}{(3^3)^2}

$$\frac { ( 3 ^ { 2 } ) ^ { 5 } \cdot 3 ^ { 3 } } { ( 3 ^ { 3 } ) ^ { 2 } }$$

Evaluate

$$2187$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

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

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

$$\frac{3^{13}}{3^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 13 to get 7.

$$3^{7}$$

Calculate 3 to the power of 7 and get 2187.

$$2187$$

Factor

$$3^{7}$$