Solve (2a^{1/3}b)^3(3a^1/2b^1/3)^2

$$( 2 a ^ { 1 / 3 } b ) ^ { 3 } ( 3 a ^ { 1 / 2 } b ^ { 1 / 3 } ) ^ { 2 }$$

Evaluate

$$72a^{2}b^{\frac{11}{3}}$$

Solution Steps

Expand \left(2a^{\frac{1}{3}}b\right)^{3}.

$$2^{3}\left(a^{\frac{1}{3}}\right)^{3}b^{3}\times \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 3 to get 1.

$$2^{3}a^{1}b^{3}\times \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8a^{1}b^{3}\times \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}$$

Calculate a to the power of 1 and get a.

$$8ab^{3}\times \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}$$

Expand \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}.

$$8ab^{3}\times 3^{2}\left(a^{\frac{1}{2}}\right)^{2}\left(b^{\frac{1}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 2 to get 1.

$$8ab^{3}\times 3^{2}a^{1}\left(b^{\frac{1}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$8ab^{3}\times 3^{2}a^{1}b^{\frac{2}{3}}$$

Calculate 3 to the power of 2 and get 9.

$$8ab^{3}\times 9a^{1}b^{\frac{2}{3}}$$

Calculate a to the power of 1 and get a.

$$8ab^{3}\times 9ab^{\frac{2}{3}}$$

Multiply 8 and 9 to get 72.

$$72ab^{3}ab^{\frac{2}{3}}$$

Multiply a and a to get a^{2}.

$$72a^{2}b^{3}b^{\frac{2}{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and \frac{2}{3} to get \frac{11}{3}.

$$72a^{2}b^{\frac{11}{3}}$$

Expand

$$72a^{2}b^{\frac{11}{3}}$$

Solution Steps

Expand \left(2a^{\frac{1}{3}}b\right)^{3}.

$$2^{3}\left(a^{\frac{1}{3}}\right)^{3}b^{3}\times \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 3 to get 1.

$$2^{3}a^{1}b^{3}\times \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8a^{1}b^{3}\times \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}$$

Calculate a to the power of 1 and get a.

$$8ab^{3}\times \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}$$

Expand \left(3a^{\frac{1}{2}}b^{\frac{1}{3}}\right)^{2}.

$$8ab^{3}\times 3^{2}\left(a^{\frac{1}{2}}\right)^{2}\left(b^{\frac{1}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 2 to get 1.

$$8ab^{3}\times 3^{2}a^{1}\left(b^{\frac{1}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$8ab^{3}\times 3^{2}a^{1}b^{\frac{2}{3}}$$

Calculate 3 to the power of 2 and get 9.

$$8ab^{3}\times 9a^{1}b^{\frac{2}{3}}$$

Calculate a to the power of 1 and get a.

$$8ab^{3}\times 9ab^{\frac{2}{3}}$$

Multiply 8 and 9 to get 72.

$$72ab^{3}ab^{\frac{2}{3}}$$

Multiply a and a to get a^{2}.

$$72a^{2}b^{3}b^{\frac{2}{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and \frac{2}{3} to get \frac{11}{3}.

$$72a^{2}b^{\frac{11}{3}}$$