Solve (7/8)^4*[(7/8)^3]^2div8/7

$$( \frac { 7 } { 8 } ) ^ { 4 } \cdot [ ( \frac { 7 } { 8 } ) ^ { 3 } ] ^ { 2 } \div \frac { 8 } { 7 }$$

Evaluate

$$\frac{1977326743}{8589934592}\approx 0.230191129$$

Solution Steps

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

$$\frac{\left(\frac{7}{8}\right)^{4}\times \left(\frac{7}{8}\right)^{6}}{\frac{8}{7}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{\left(\frac{7}{8}\right)^{10}}{\frac{8}{7}}$$

Calculate \frac{7}{8} to the power of 10 and get \frac{282475249}{1073741824}.

$$\frac{\frac{282475249}{1073741824}}{\frac{8}{7}}$$

Divide \frac{282475249}{1073741824} by \frac{8}{7} by multiplying \frac{282475249}{1073741824} by the reciprocal of \frac{8}{7}.

$$\frac{282475249}{1073741824}\times \frac{7}{8}$$

Multiply \frac{282475249}{1073741824} and \frac{7}{8} to get \frac{1977326743}{8589934592}.

$$\frac{1977326743}{8589934592}$$

Factor

$$\frac{7 ^ {11}}{2 ^ {33}} = 0.23019112914334983$$