Solve (-9a^2b)*(2/3ab^3)^2=

$$( - 9 a ^ { 2 } b ) \cdot ( \frac { 2 } { 3 } a b ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$-4a^{4}b^{7}$$

Solution Steps

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

$$-9a^{2}b\times \left(\frac{2}{3}\right)^{2}a^{2}\left(b^{3}\right)^{2}$$

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

$$-9a^{2}b\times \left(\frac{2}{3}\right)^{2}a^{2}b^{6}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-9a^{2}b\times \frac{4}{9}a^{2}b^{6}$$

Multiply -9 and \frac{4}{9} to get -4.

$$-4a^{2}ba^{2}b^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-4a^{4}bb^{6}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$-4a^{4}b^{7}$$

Expand

$$-4a^{4}b^{7}$$

Solution Steps

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

$$-9a^{2}b\times \left(\frac{2}{3}\right)^{2}a^{2}\left(b^{3}\right)^{2}$$

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

$$-9a^{2}b\times \left(\frac{2}{3}\right)^{2}a^{2}b^{6}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-9a^{2}b\times \frac{4}{9}a^{2}b^{6}$$

Multiply -9 and \frac{4}{9} to get -4.

$$-4a^{2}ba^{2}b^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-4a^{4}bb^{6}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$-4a^{4}b^{7}$$