Solve (b^{3}c^0d^-2e^4)^2

$$( b ^ { 3 } c ^ { 0 } d ^ { - 2 } e ^ { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{e^{8}b^{6}}{d^{4}}$$

Solution Steps

Calculate c to the power of 0 and get 1.

$$\left(b^{3}\times 1d^{-2}e^{4}\right)^{2}$$

Expand \left(b^{3}\times 1d^{-2}e^{4}\right)^{2}.

$$\left(b^{3}\right)^{2}\times 1^{2}\left(d^{-2}\right)^{2}\left(e^{4}\right)^{2}$$

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

$$b^{6}\times 1^{2}\left(d^{-2}\right)^{2}\left(e^{4}\right)^{2}$$

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

$$b^{6}\times 1^{2}d^{-4}\left(e^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$b^{6}\times 1^{2}d^{-4}e^{8}$$

Calculate 1 to the power of 2 and get 1.

$$b^{6}\times 1d^{-4}e^{8}$$

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

$$b^{6}d^{-4}e^{8}$$

Expand

$$\frac{e^{8}b^{6}}{d^{4}}$$

Solution Steps

Calculate c to the power of 0 and get 1.

$$\left(b^{3}\times 1d^{-2}e^{4}\right)^{2}$$

Expand \left(b^{3}\times 1d^{-2}e^{4}\right)^{2}.

$$\left(b^{3}\right)^{2}\times 1^{2}\left(d^{-2}\right)^{2}\left(e^{4}\right)^{2}$$

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

$$b^{6}\times 1^{2}\left(d^{-2}\right)^{2}\left(e^{4}\right)^{2}$$

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

$$b^{6}\times 1^{2}d^{-4}\left(e^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$b^{6}\times 1^{2}d^{-4}e^{8}$$

Calculate 1 to the power of 2 and get 1.

$$b^{6}\times 1d^{-4}e^{8}$$

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

$$b^{6}d^{-4}e^{8}$$