Solve (3a^4b^4/8c^2)^4

$$( \frac { 3 a ^ { 4 } b ^ { 4 } } { 8 c ^ { 2 } } ) ^ { 4 }$$

Evaluate

$$\frac{81\left(ab\right)^{16}}{4096c^{8}}$$

Solution Steps

To raise \frac{3a^{4}b^{4}}{8c^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3a^{4}b^{4}\right)^{4}}{\left(8c^{2}\right)^{4}}$$

Expand \left(3a^{4}b^{4}\right)^{4}.

$$\frac{3^{4}\left(a^{4}\right)^{4}\left(b^{4}\right)^{4}}{\left(8c^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{3^{4}a^{16}\left(b^{4}\right)^{4}}{\left(8c^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{3^{4}a^{16}b^{16}}{\left(8c^{2}\right)^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81a^{16}b^{16}}{\left(8c^{2}\right)^{4}}$$

Expand \left(8c^{2}\right)^{4}.

$$\frac{81a^{16}b^{16}}{8^{4}\left(c^{2}\right)^{4}}$$

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

$$\frac{81a^{16}b^{16}}{8^{4}c^{8}}$$

Calculate 8 to the power of 4 and get 4096.

$$\frac{81a^{16}b^{16}}{4096c^{8}}$$

Expand

$$\frac{81\left(ab\right)^{16}}{4096c^{8}}$$

Solution Steps

To raise \frac{3a^{4}b^{4}}{8c^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3a^{4}b^{4}\right)^{4}}{\left(8c^{2}\right)^{4}}$$

Expand \left(3a^{4}b^{4}\right)^{4}.

$$\frac{3^{4}\left(a^{4}\right)^{4}\left(b^{4}\right)^{4}}{\left(8c^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{3^{4}a^{16}\left(b^{4}\right)^{4}}{\left(8c^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{3^{4}a^{16}b^{16}}{\left(8c^{2}\right)^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81a^{16}b^{16}}{\left(8c^{2}\right)^{4}}$$

Expand \left(8c^{2}\right)^{4}.

$$\frac{81a^{16}b^{16}}{8^{4}\left(c^{2}\right)^{4}}$$

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

$$\frac{81a^{16}b^{16}}{8^{4}c^{8}}$$

Calculate 8 to the power of 4 and get 4096.

$$\frac{81a^{16}b^{16}}{4096c^{8}}$$