Solve frac{2^{-2}*2^{2}+2*(3^2)^2+18^0}{8^2/3}é

$$\frac { 2 ^ { - 2 } \cdot 2 ^ { 2 } + 2 \cdot ( 3 ^ { 2 } ) ^ { 2 } + 18 ^ { 0 } } { 8 ^ { 2 / 3 } } é$$

Evaluate

$$41é$$

Solution Steps

Multiply 2^{-2} and 2^{2} to get 1.

$$\frac{1+2\times \left(3^{2}\right)^{2}+18^{0}}{8^{\frac{2}{3}}}é$$

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

$$\frac{1+2\times 3^{4}+18^{0}}{8^{\frac{2}{3}}}é$$

Calculate 3 to the power of 4 and get 81.

$$\frac{1+2\times 81+18^{0}}{8^{\frac{2}{3}}}é$$

Multiply 2 and 81 to get 162.

$$\frac{1+162+18^{0}}{8^{\frac{2}{3}}}é$$

Add 1 and 162 to get 163.

$$\frac{163+18^{0}}{8^{\frac{2}{3}}}é$$

Calculate 18 to the power of 0 and get 1.

$$\frac{163+1}{8^{\frac{2}{3}}}é$$

Add 163 and 1 to get 164.

$$\frac{164}{8^{\frac{2}{3}}}é$$

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

$$\frac{164}{4}é$$

Divide 164 by 4 to get 41.

$$41é$$

Differentiate w.r.t. é

$$41$$

Steps Using Definition of a Derivative

Multiply 2^{-2} and 2^{2} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\frac{1+2\times \left(3^{2}\right)^{2}+18^{0}}{8^{\frac{2}{3}}}é)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}é}(\frac{1+2\times 3^{4}+18^{0}}{8^{\frac{2}{3}}}é)$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\frac{1+2\times 81+18^{0}}{8^{\frac{2}{3}}}é)$$

Multiply 2 and 81 to get 162.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\frac{1+162+18^{0}}{8^{\frac{2}{3}}}é)$$

Add 1 and 162 to get 163.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\frac{163+18^{0}}{8^{\frac{2}{3}}}é)$$

Calculate 18 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\frac{163+1}{8^{\frac{2}{3}}}é)$$

Add 163 and 1 to get 164.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\frac{164}{8^{\frac{2}{3}}}é)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}é}(\frac{164}{4}é)$$

Divide 164 by 4 to get 41.

$$\frac{\mathrm{d}}{\mathrm{d}é}(41é)$$

The derivative of ax^{n} is nax^{n-1}.

$$41é^{1-1}$$

Subtract 1 from 1.

$$41é^{0}$$

For any term t except 0, t^{0}=1.

$$41\times 1$$

For any term t, t\times 1=t and 1t=t.

$$41$$