Solve (2a^5bc^4/d^2e)^5

$$( \frac { 2 a ^ { 5 } b c ^ { 4 } } { d ^ { 2 } e } ) ^ { 5 }$$

Evaluate

$$\frac{32\times \left(\frac{b}{e}\right)^{5}c^{20}a^{25}}{d^{10}}$$

Solution Steps

To raise \frac{2a^{5}bc^{4}}{d^{2}e} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2a^{5}bc^{4}\right)^{5}}{\left(d^{2}e\right)^{5}}$$

Expand \left(2a^{5}bc^{4}\right)^{5}.

$$\frac{2^{5}\left(a^{5}\right)^{5}b^{5}\left(c^{4}\right)^{5}}{\left(d^{2}e\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{2^{5}a^{25}b^{5}\left(c^{4}\right)^{5}}{\left(d^{2}e\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{2^{5}a^{25}b^{5}c^{20}}{\left(d^{2}e\right)^{5}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32a^{25}b^{5}c^{20}}{\left(d^{2}e\right)^{5}}$$

Expand \left(d^{2}e\right)^{5}.

$$\frac{32a^{25}b^{5}c^{20}}{\left(d^{2}\right)^{5}e^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{32a^{25}b^{5}c^{20}}{d^{10}e^{5}}$$

Expand

$$\frac{32\times \left(\frac{b}{e}\right)^{5}c^{20}a^{25}}{d^{10}}$$

Solution Steps

To raise \frac{2a^{5}bc^{4}}{d^{2}e} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2a^{5}bc^{4}\right)^{5}}{\left(d^{2}e\right)^{5}}$$

Expand \left(2a^{5}bc^{4}\right)^{5}.

$$\frac{2^{5}\left(a^{5}\right)^{5}b^{5}\left(c^{4}\right)^{5}}{\left(d^{2}e\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{2^{5}a^{25}b^{5}\left(c^{4}\right)^{5}}{\left(d^{2}e\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{2^{5}a^{25}b^{5}c^{20}}{\left(d^{2}e\right)^{5}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32a^{25}b^{5}c^{20}}{\left(d^{2}e\right)^{5}}$$

Expand \left(d^{2}e\right)^{5}.

$$\frac{32a^{25}b^{5}c^{20}}{\left(d^{2}\right)^{5}e^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{32a^{25}b^{5}c^{20}}{d^{10}e^{5}}$$