Solve (-3)^200x(2/3)^200

$$( - 3 ) ^ { 200 } x ( \frac { 2 } { 3 } ) ^ { 200 }$$

Evaluate

$$1606938044258990275541962092341162602522202993782792835301376x$$

Solution Steps

Calculate -3 to the power of 200 and get 265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001.

$$265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001x\times \left(\frac{2}{3}\right)^{200}$$

Calculate \frac{2}{3} to the power of 200 and get \frac{1606938044258990275541962092341162602522202993782792835301376}{265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001}.

$$265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001x\times \frac{1606938044258990275541962092341162602522202993782792835301376}{265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001}$$

Cancel out 265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001 and 265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001.

$$1606938044258990275541962092341162602522202993782792835301376x$$

Differentiate w.r.t. x

$$1606938044258990275541962092341162602522202993782792835301376$$

Steps Using Definition of a Derivative

Calculate -3 to the power of 200 and get 265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001.

$$\frac{\mathrm{d}}{\mathrm{d}x}(265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001x\times \left(\frac{2}{3}\right)^{200})$$

Calculate \frac{2}{3} to the power of 200 and get \frac{1606938044258990275541962092341162602522202993782792835301376}{265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001x\times \frac{1606938044258990275541962092341162602522202993782792835301376}{265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001})$$

Cancel out 265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001 and 265613988875874769338781322035779626829233452653394495974574961739092490901302182994384699044001.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1606938044258990275541962092341162602522202993782792835301376x)$$

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

$$1606938044258990275541962092341162602522202993782792835301376x^{1-1}$$

Subtract 1 from 1.

$$1606938044258990275541962092341162602522202993782792835301376x^{0}$$

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

$$1606938044258990275541962092341162602522202993782792835301376\times 1$$

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

$$1606938044258990275541962092341162602522202993782792835301376$$