Solve 7*(7/8)^5-8*(7/8)^6

$$7 \times ( \frac { 7 } { 8 } ) ^ { 5 } - 8 \times ( \frac { 7 } { 8 } ) ^ { 6 }$$

Evaluate

$$0$$

Solution Steps

Calculate \frac{7}{8} to the power of 5 and get \frac{16807}{32768}.

$$7\times \frac{16807}{32768}-8\times \left(\frac{7}{8}\right)^{6}$$

Express 7\times \frac{16807}{32768} as a single fraction.

$$\frac{7\times 16807}{32768}-8\times \left(\frac{7}{8}\right)^{6}$$

Multiply 7 and 16807 to get 117649.

$$\frac{117649}{32768}-8\times \left(\frac{7}{8}\right)^{6}$$

Calculate \frac{7}{8} to the power of 6 and get \frac{117649}{262144}.

$$\frac{117649}{32768}-8\times \frac{117649}{262144}$$

Express 8\times \frac{117649}{262144} as a single fraction.

$$\frac{117649}{32768}-\frac{8\times 117649}{262144}$$

Multiply 8 and 117649 to get 941192.

$$\frac{117649}{32768}-\frac{941192}{262144}$$

Reduce the fraction \frac{941192}{262144} to lowest terms by extracting and canceling out 8.

$$\frac{117649}{32768}-\frac{117649}{32768}$$

Subtract \frac{117649}{32768} from \frac{117649}{32768} to get 0.

$$0$$

Factor

$$0$$