Solve frac{2^{-1}*2^{4}+2*(3^2)^-2+13^0}{8^frac{2{3}}}

$$\frac { 2 ^ { - 1 } \cdot 2 ^ { 4 } + 2 \cdot ( 3 ^ { 2 } ) ^ { - 2 } + 13 ^ { 0 } } { 8 ^ { \frac { 2 } { 3 } } }$$

Evaluate

$$\frac{731}{324}\approx 2.25617284$$

Solution Steps

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

$$\frac{2^{3}+2\times \left(3^{2}\right)^{-2}+13^{0}}{8^{\frac{2}{3}}}$$

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

$$\frac{2^{3}+2\times 3^{-4}+13^{0}}{8^{\frac{2}{3}}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8+2\times 3^{-4}+13^{0}}{8^{\frac{2}{3}}}$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{8+2\times \frac{1}{81}+13^{0}}{8^{\frac{2}{3}}}$$

Multiply 2 and \frac{1}{81} to get \frac{2}{81}.

$$\frac{8+\frac{2}{81}+13^{0}}{8^{\frac{2}{3}}}$$

Add 8 and \frac{2}{81} to get \frac{650}{81}.

$$\frac{\frac{650}{81}+13^{0}}{8^{\frac{2}{3}}}$$

Calculate 13 to the power of 0 and get 1.

$$\frac{\frac{650}{81}+1}{8^{\frac{2}{3}}}$$

Add \frac{650}{81} and 1 to get \frac{731}{81}.

$$\frac{\frac{731}{81}}{8^{\frac{2}{3}}}$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$\frac{\frac{731}{81}}{4}$$

Express \frac{\frac{731}{81}}{4} as a single fraction.

$$\frac{731}{81\times 4}$$

Multiply 81 and 4 to get 324.

$$\frac{731}{324}$$

Factor

$$\frac{17 \cdot 43}{2 ^ {2} \cdot 3 ^ {4}} = 2\frac{83}{324} = 2.256172839506173$$