Solve [(3/2)^{2}]^2+(1/2)^3*(1/2)^2*1/2-(frac{1}{4})^3*frac{1}{4}=

$$[ ( \frac { 3 } { 2 } ) ^ { 2 } ] ^ { 2 } + ( \frac { 1 } { 2 } ) ^ { 3 } \cdot ( \frac { 1 } { 2 } ) ^ { 2 } \cdot \frac { 1 } { 2 } - ( \frac { 1 } { 4 } ) ^ { 3 } \cdot \frac { 1 } { 4 } =$$

Evaluate

$$\frac{1299}{256}=5.07421875$$

Solution Steps

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

$$\left(\frac{3}{2}\right)^{4}+\left(\frac{1}{2}\right)^{3}\times \left(\frac{1}{2}\right)^{2}\times \frac{1}{2}-\left(\frac{1}{4}\right)^{3}\times \frac{1}{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(\frac{3}{2}\right)^{4}+\left(\frac{1}{2}\right)^{5}\times \frac{1}{2}-\left(\frac{1}{4}\right)^{3}\times \frac{1}{4}$$

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

$$\left(\frac{3}{2}\right)^{4}+\left(\frac{1}{2}\right)^{6}-\left(\frac{1}{4}\right)^{3}\times \frac{1}{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(\frac{3}{2}\right)^{4}+\left(\frac{1}{2}\right)^{6}-\left(\frac{1}{4}\right)^{4}$$

Calculate \frac{3}{2} to the power of 4 and get \frac{81}{16}.

$$\frac{81}{16}+\left(\frac{1}{2}\right)^{6}-\left(\frac{1}{4}\right)^{4}$$

Calculate \frac{1}{2} to the power of 6 and get \frac{1}{64}.

$$\frac{81}{16}+\frac{1}{64}-\left(\frac{1}{4}\right)^{4}$$

Add \frac{81}{16} and \frac{1}{64} to get \frac{325}{64}.

$$\frac{325}{64}-\left(\frac{1}{4}\right)^{4}$$

Calculate \frac{1}{4} to the power of 4 and get \frac{1}{256}.

$$\frac{325}{64}-\frac{1}{256}$$

Subtract \frac{1}{256} from \frac{325}{64} to get \frac{1299}{256}.

$$\frac{1299}{256}$$

Factor

$$\frac{3 \cdot 433}{2 ^ {8}} = 5\frac{19}{256} = 5.07421875$$