Solve frac{(2a^{2}b^{3})^3(a^3)^2}{2a^3}=

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

Evaluate

$$4\left(ab\right)^{9}$$

Solution Steps

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

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

Calculate 2 to the power of 3 and get 8.

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

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{a^{9}\times 8b^{9}}{2}$$

Divide a^{9}\times 8b^{9} by 2 to get a^{9}\times 4b^{9}.

$$a^{9}\times 4b^{9}$$

Expand

$$4\left(ab\right)^{9}$$

Solution Steps

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

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

Calculate 2 to the power of 3 and get 8.

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

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{a^{9}\times 8b^{9}}{2}$$

Divide a^{9}\times 8b^{9} by 2 to get a^{9}\times 4b^{9}.

$$a^{9}\times 4b^{9}$$