Solve (2a^3b^6/8b^3)^2

$$( \frac { 2 a ^ { 3 } b ^ { 6 } } { 8 b ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{\left(ab\right)^{6}}{16}$$

Solution Steps

Cancel out 2b^{3} in both numerator and denominator.

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

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

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

Expand \left(a^{3}b^{3}\right)^{2}.

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

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

$$\frac{a^{6}\left(b^{3}\right)^{2}}{4^{2}}$$

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

$$\frac{a^{6}b^{6}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{a^{6}b^{6}}{16}$$

Expand

$$\frac{\left(ab\right)^{6}}{16}$$

Solution Steps

Cancel out 2b^{3} in both numerator and denominator.

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

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

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

Expand \left(a^{3}b^{3}\right)^{2}.

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

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

$$\frac{a^{6}\left(b^{3}\right)^{2}}{4^{2}}$$

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

$$\frac{a^{6}b^{6}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{a^{6}b^{6}}{16}$$