Solve 8([11/4)^2]^3}^2

$$8 ( [ 1 \frac { 1 } { 4 } ) ^ { 2 } ] ^ { 3 } \} ^ { 2 }$$

Evaluate

$$\frac{15625}{512}=30.517578125$$

Solution Steps

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

$$8\times \left(\frac{1\times 4+1}{4}\right)^{6}$$

Multiply 1 and 4 to get 4.

$$8\times \left(\frac{4+1}{4}\right)^{6}$$

Add 4 and 1 to get 5.

$$8\times \left(\frac{5}{4}\right)^{6}$$

Calculate \frac{5}{4} to the power of 6 and get \frac{15625}{4096}.

$$8\times \frac{15625}{4096}$$

Multiply 8 and \frac{15625}{4096} to get \frac{15625}{512}.

$$\frac{15625}{512}$$

Factor

$$\frac{5 ^ {6}}{2 ^ {9}} = 30\frac{265}{512} = 30.517578125$$