Solve (2a^2b^5/5c^3)^2

$$( \frac { 2 a ^ { 2 } b ^ { 5 } } { 5 c ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{4a^{4}b^{10}}{25c^{6}}$$

Solution Steps

To raise \frac{2a^{2}b^{5}}{5c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2a^{2}b^{5}\right)^{2}}{\left(5c^{3}\right)^{2}}$$

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

$$\frac{2^{2}\left(a^{2}\right)^{2}\left(b^{5}\right)^{2}}{\left(5c^{3}\right)^{2}}$$

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

$$\frac{2^{2}a^{4}\left(b^{5}\right)^{2}}{\left(5c^{3}\right)^{2}}$$

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

$$\frac{2^{2}a^{4}b^{10}}{\left(5c^{3}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{4}b^{10}}{\left(5c^{3}\right)^{2}}$$

Expand \left(5c^{3}\right)^{2}.

$$\frac{4a^{4}b^{10}}{5^{2}\left(c^{3}\right)^{2}}$$

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

$$\frac{4a^{4}b^{10}}{5^{2}c^{6}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4a^{4}b^{10}}{25c^{6}}$$

Expand

$$\frac{4a^{4}b^{10}}{25c^{6}}$$

Solution Steps

To raise \frac{2a^{2}b^{5}}{5c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2a^{2}b^{5}\right)^{2}}{\left(5c^{3}\right)^{2}}$$

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

$$\frac{2^{2}\left(a^{2}\right)^{2}\left(b^{5}\right)^{2}}{\left(5c^{3}\right)^{2}}$$

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

$$\frac{2^{2}a^{4}\left(b^{5}\right)^{2}}{\left(5c^{3}\right)^{2}}$$

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

$$\frac{2^{2}a^{4}b^{10}}{\left(5c^{3}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{4}b^{10}}{\left(5c^{3}\right)^{2}}$$

Expand \left(5c^{3}\right)^{2}.

$$\frac{4a^{4}b^{10}}{5^{2}\left(c^{3}\right)^{2}}$$

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

$$\frac{4a^{4}b^{10}}{5^{2}c^{6}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4a^{4}b^{10}}{25c^{6}}$$