Solve (3^{4}:3^{3})^2*(3^7:3^5)^2

$$( 3 ^ { 4 } : 3 ^ { 3 } ) ^ { 2 } \cdot ( 3 ^ { 7 } : 3 ^ { 5 } ) ^ { 2 }$$

Evaluate

$$729$$

Solution Steps

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

$$\left(3^{1}\right)^{2}\times \left(\frac{3^{7}}{3^{5}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 1 and 2 to get 2.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 to get 2.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$3^{2}\times 3^{4}$$

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

$$3^{6}$$

Calculate 3 to the power of 6 and get 729.

$$729$$

Factor

$$3^{6}$$