Solve (-3a^5b^2)^2*(3ab^2)

$$( - 3 a ^ { 5 } b ^ { 2 } ) ^ { 2 } \cdot ( 3 a b ^ { 2 } )$$

Evaluate

$$27b^{6}a^{11}$$

Solution Steps

Expand \left(-3a^{5}b^{2}\right)^{2}.

$$\left(-3\right)^{2}\left(a^{5}\right)^{2}\left(b^{2}\right)^{2}\times 3ab^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\left(-3\right)^{2}a^{10}\left(b^{2}\right)^{2}\times 3ab^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-3\right)^{2}a^{10}b^{4}\times 3ab^{2}$$

Calculate -3 to the power of 2 and get 9.

$$9a^{10}b^{4}\times 3ab^{2}$$

Multiply 9 and 3 to get 27.

$$27a^{10}b^{4}ab^{2}$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$27a^{11}b^{4}b^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$27a^{11}b^{6}$$

Expand

$$27b^{6}a^{11}$$

Solution Steps

Expand \left(-3a^{5}b^{2}\right)^{2}.

$$\left(-3\right)^{2}\left(a^{5}\right)^{2}\left(b^{2}\right)^{2}\times 3ab^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\left(-3\right)^{2}a^{10}\left(b^{2}\right)^{2}\times 3ab^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-3\right)^{2}a^{10}b^{4}\times 3ab^{2}$$

Calculate -3 to the power of 2 and get 9.

$$9a^{10}b^{4}\times 3ab^{2}$$

Multiply 9 and 3 to get 27.

$$27a^{10}b^{4}ab^{2}$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$27a^{11}b^{4}b^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$27a^{11}b^{6}$$