Solve (5a^4b^4/10a^2)^4

$$( \frac { 5 a ^ { 4 } b ^ { 4 } } { 10 a ^ { 2 } } ) ^ { 4 }$$

Evaluate

$$\frac{a^{8}b^{16}}{16}$$

Solution Steps

Cancel out 5a^{2} in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{a^{8}b^{16}}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{a^{8}b^{16}}{16}$$

Expand

$$\frac{a^{8}b^{16}}{16}$$

Solution Steps

Cancel out 5a^{2} in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{a^{8}b^{16}}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{a^{8}b^{16}}{16}$$