Solve (2^{2}a^2)^3(2ab^3)^-1

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

Evaluate

$$\frac{32a^{5}}{b^{3}}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\left(4a^{2}\right)^{3}\times \left(2ab^{3}\right)^{-1}$$

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

$$4^{3}\left(a^{2}\right)^{3}\times \left(2ab^{3}\right)^{-1}$$

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

$$4^{3}a^{6}\times \left(2ab^{3}\right)^{-1}$$

Calculate 4 to the power of 3 and get 64.

$$64a^{6}\times \left(2ab^{3}\right)^{-1}$$

Expand \left(2ab^{3}\right)^{-1}.

$$64a^{6}\times 2^{-1}a^{-1}\left(b^{3}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$64a^{6}\times 2^{-1}a^{-1}b^{-3}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$64a^{6}\times \frac{1}{2}a^{-1}b^{-3}$$

Multiply 64 and \frac{1}{2} to get 32.

$$32a^{6}a^{-1}b^{-3}$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$32a^{5}b^{-3}$$

Expand

$$\frac{32a^{5}}{b^{3}}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\left(4a^{2}\right)^{3}\times \left(2ab^{3}\right)^{-1}$$

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

$$4^{3}\left(a^{2}\right)^{3}\times \left(2ab^{3}\right)^{-1}$$

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

$$4^{3}a^{6}\times \left(2ab^{3}\right)^{-1}$$

Calculate 4 to the power of 3 and get 64.

$$64a^{6}\times \left(2ab^{3}\right)^{-1}$$

Expand \left(2ab^{3}\right)^{-1}.

$$64a^{6}\times 2^{-1}a^{-1}\left(b^{3}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$64a^{6}\times 2^{-1}a^{-1}b^{-3}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$64a^{6}\times \frac{1}{2}a^{-1}b^{-3}$$

Multiply 64 and \frac{1}{2} to get 32.

$$32a^{6}a^{-1}b^{-3}$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$32a^{5}b^{-3}$$