Solve 6a^{3}b^2div(3a^4b^5)^2=

$$6 a ^ { 3 } b ^ { 2 } \div ( 3 a ^ { 4 } b ^ { 5 } ) ^ { 2 } =$$

Evaluate

$$\frac{2}{3a^{5}b^{8}}$$

Solution Steps

Expand \left(3a^{4}b^{5}\right)^{2}.

$$\frac{6a^{3}b^{2}}{3^{2}\left(a^{4}\right)^{2}\left(b^{5}\right)^{2}}$$

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

$$\frac{6a^{3}b^{2}}{3^{2}a^{8}\left(b^{5}\right)^{2}}$$

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

$$\frac{6a^{3}b^{2}}{3^{2}a^{8}b^{10}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{6a^{3}b^{2}}{9a^{8}b^{10}}$$

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

$$\frac{2}{3a^{5}b^{8}}$$

Expand

$$\frac{2}{3a^{5}b^{8}}$$

Solution Steps

Expand \left(3a^{4}b^{5}\right)^{2}.

$$\frac{6a^{3}b^{2}}{3^{2}\left(a^{4}\right)^{2}\left(b^{5}\right)^{2}}$$

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

$$\frac{6a^{3}b^{2}}{3^{2}a^{8}\left(b^{5}\right)^{2}}$$

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

$$\frac{6a^{3}b^{2}}{3^{2}a^{8}b^{10}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{6a^{3}b^{2}}{9a^{8}b^{10}}$$

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

$$\frac{2}{3a^{5}b^{8}}$$