Solve (-3a^{2}b^{3})^2*(-a^3b^2)^5

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

Evaluate

$$-9b^{16}a^{19}$$

Solution Steps

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

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

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

$$\left(-3\right)^{2}a^{4}\left(b^{3}\right)^{2}\left(\left(-a^{3}\right)b^{2}\right)^{5}$$

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

$$\left(-3\right)^{2}a^{4}b^{6}\left(\left(-a^{3}\right)b^{2}\right)^{5}$$

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

$$9a^{4}b^{6}\left(\left(-a^{3}\right)b^{2}\right)^{5}$$

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

$$9a^{4}b^{6}\left(-a^{3}\right)^{5}\left(b^{2}\right)^{5}$$

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

$$9a^{4}b^{6}\left(-a^{3}\right)^{5}b^{10}$$

To multiply powers of the same base, add their exponents. Add 6 and 10 to get 16.

$$9a^{4}b^{16}\left(-a^{3}\right)^{5}$$

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

$$9a^{4}b^{16}\left(-1\right)^{5}\left(a^{3}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$9a^{4}b^{16}\left(-1\right)^{5}a^{15}$$

Calculate -1 to the power of 5 and get -1.

$$9a^{4}b^{16}\left(-1\right)a^{15}$$

Multiply 9 and -1 to get -9.

$$-9a^{4}b^{16}a^{15}$$

To multiply powers of the same base, add their exponents. Add 4 and 15 to get 19.

$$-9a^{19}b^{16}$$

Expand

$$-9b^{16}a^{19}$$

Solution Steps

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

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

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

$$\left(-3\right)^{2}a^{4}\left(b^{3}\right)^{2}\left(\left(-a^{3}\right)b^{2}\right)^{5}$$

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

$$\left(-3\right)^{2}a^{4}b^{6}\left(\left(-a^{3}\right)b^{2}\right)^{5}$$

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

$$9a^{4}b^{6}\left(\left(-a^{3}\right)b^{2}\right)^{5}$$

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

$$9a^{4}b^{6}\left(-a^{3}\right)^{5}\left(b^{2}\right)^{5}$$

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

$$9a^{4}b^{6}\left(-a^{3}\right)^{5}b^{10}$$

To multiply powers of the same base, add their exponents. Add 6 and 10 to get 16.

$$9a^{4}b^{16}\left(-a^{3}\right)^{5}$$

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

$$9a^{4}b^{16}\left(-1\right)^{5}\left(a^{3}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$9a^{4}b^{16}\left(-1\right)^{5}a^{15}$$

Calculate -1 to the power of 5 and get -1.

$$9a^{4}b^{16}\left(-1\right)a^{15}$$

Multiply 9 and -1 to get -9.

$$-9a^{4}b^{16}a^{15}$$

To multiply powers of the same base, add their exponents. Add 4 and 15 to get 19.

$$-9a^{19}b^{16}$$