Solve 3a^2b*(2ab^-2)^3

$$3 a ^ { 2 } b \times ( 2 a b ^ { - 2 } ) ^ { 3 }$$

Evaluate

$$24\times \left(\frac{a}{b}\right)^{5}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 3 and 8 to get 24.

$$24a^{2}ba^{3}b^{-6}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$24a^{5}bb^{-6}$$

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

$$24a^{5}b^{-5}$$

Expand

$$24\times \left(\frac{a}{b}\right)^{5}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 3 and 8 to get 24.

$$24a^{2}ba^{3}b^{-6}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$24a^{5}bb^{-6}$$

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

$$24a^{5}b^{-5}$$