Solve [(+7/4)^3*(+7/4)^8]:[(+7/4)^5*(+7/4)]

$$[ ( + \frac { 7 } { 4 } ) ^ { 3 } \cdot ( + \frac { 7 } { 4 } ) ^ { 8 } ] : [ ( + \frac { 7 } { 4 } ) ^ { 5 } \cdot ( + \frac { 7 } { 4 } ) ]$$

Evaluate

$$\frac{16807}{1024}\approx 16.413085938$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\frac{\left(\frac{7}{4}\right)^{11}}{\left(\frac{7}{4}\right)^{5}\times \frac{7}{4}}$$

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

$$\frac{\left(\frac{7}{4}\right)^{11}}{\left(\frac{7}{4}\right)^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 11 to get 5.

$$\left(\frac{7}{4}\right)^{5}$$

Calculate \frac{7}{4} to the power of 5 and get \frac{16807}{1024}.

$$\frac{16807}{1024}$$

Factor

$$\frac{7 ^ {5}}{2 ^ {10}} = 16\frac{423}{1024} = 16.4130859375$$