Solve 32a^6b^6/{left(4a^2b^2right)^2}

$$\frac{ 32 { a }^{ 6 } { b }^{ 6 } }{ { \left(4 { a }^{ 2 } { b }^{ 2 } \right) }^{ 2 } }$$

Evaluate

$$2\left(ab\right)^{2}$$

Solution Steps

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

$$\frac{32a^{6}b^{6}}{4^{2}\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}}$$

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

$$\frac{32a^{6}b^{6}}{4^{2}a^{4}\left(b^{2}\right)^{2}}$$

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

$$\frac{32a^{6}b^{6}}{4^{2}a^{4}b^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{32a^{6}b^{6}}{16a^{4}b^{4}}$$

Cancel out 16a^{4}b^{4} in both numerator and denominator.

$$2a^{2}b^{2}$$

Expand

$$2\left(ab\right)^{2}$$

Solution Steps

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

$$\frac{32a^{6}b^{6}}{4^{2}\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}}$$

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

$$\frac{32a^{6}b^{6}}{4^{2}a^{4}\left(b^{2}\right)^{2}}$$

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

$$\frac{32a^{6}b^{6}}{4^{2}a^{4}b^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{32a^{6}b^{6}}{16a^{4}b^{4}}$$

Cancel out 16a^{4}b^{4} in both numerator and denominator.

$$2a^{2}b^{2}$$