Solve frac{(2d^{2}e^{3})^{4}*(-8de^{-2})^2}{4de^5*12d^9e^7}

$$\frac { ( 2 d ^ { 2 } e ^ { 3 } ) ^ { 4 } \cdot ( - 8 d e ^ { - 2 } ) ^ { 2 } } { 4 d e ^ { 5 } \times 12 d ^ { 9 } e ^ { 7 } }$$

Evaluate

$$\frac{64}{3e^{4}}\approx 0.39073363$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$\frac{\left(2d^{2}e^{3}\right)^{4}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{5}\times 12e^{7}}$$

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$\frac{\left(2d^{2}e^{3}\right)^{4}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

Expand \left(2d^{2}e^{3}\right)^{4}.

$$\frac{2^{4}\left(d^{2}\right)^{4}\left(e^{3}\right)^{4}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

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

$$\frac{2^{4}d^{8}\left(e^{3}\right)^{4}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{2^{4}d^{8}e^{12}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16d^{8}e^{12}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

Expand \left(-8de^{-2}\right)^{2}.

$$\frac{16d^{8}e^{12}\left(-8\right)^{2}d^{2}\left(e^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

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

$$\frac{16d^{8}e^{12}\left(-8\right)^{2}d^{2}e^{-4}}{4d^{10}e^{12}\times 12}$$

Calculate -8 to the power of 2 and get 64.

$$\frac{16d^{8}e^{12}\times 64d^{2}e^{-4}}{4d^{10}e^{12}\times 12}$$

Multiply 16 and 64 to get 1024.

$$\frac{1024d^{8}e^{12}d^{2}e^{-4}}{4d^{10}e^{12}\times 12}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{1024d^{10}e^{12}e^{-4}}{4d^{10}e^{12}\times 12}$$

To multiply powers of the same base, add their exponents. Add 12 and -4 to get 8.

$$\frac{1024d^{10}e^{8}}{4d^{10}e^{12}\times 12}$$

Multiply 4 and 12 to get 48.

$$\frac{1024d^{10}e^{8}}{48d^{10}e^{12}}$$

Cancel out 16e^{8}d^{10} in both numerator and denominator.

$$\frac{64}{3e^{4}}$$

Expand

$$\frac{64}{3e^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$\frac{\left(2d^{2}e^{3}\right)^{4}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{5}\times 12e^{7}}$$

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$\frac{\left(2d^{2}e^{3}\right)^{4}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

Expand \left(2d^{2}e^{3}\right)^{4}.

$$\frac{2^{4}\left(d^{2}\right)^{4}\left(e^{3}\right)^{4}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

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

$$\frac{2^{4}d^{8}\left(e^{3}\right)^{4}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{2^{4}d^{8}e^{12}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16d^{8}e^{12}\left(-8de^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

Expand \left(-8de^{-2}\right)^{2}.

$$\frac{16d^{8}e^{12}\left(-8\right)^{2}d^{2}\left(e^{-2}\right)^{2}}{4d^{10}e^{12}\times 12}$$

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

$$\frac{16d^{8}e^{12}\left(-8\right)^{2}d^{2}e^{-4}}{4d^{10}e^{12}\times 12}$$

Calculate -8 to the power of 2 and get 64.

$$\frac{16d^{8}e^{12}\times 64d^{2}e^{-4}}{4d^{10}e^{12}\times 12}$$

Multiply 16 and 64 to get 1024.

$$\frac{1024d^{8}e^{12}d^{2}e^{-4}}{4d^{10}e^{12}\times 12}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{1024d^{10}e^{12}e^{-4}}{4d^{10}e^{12}\times 12}$$

To multiply powers of the same base, add their exponents. Add 12 and -4 to get 8.

$$\frac{1024d^{10}e^{8}}{4d^{10}e^{12}\times 12}$$

Multiply 4 and 12 to get 48.

$$\frac{1024d^{10}e^{8}}{48d^{10}e^{12}}$$

Cancel out 16e^{8}d^{10} in both numerator and denominator.

$$\frac{64}{3e^{4}}$$