Solve (-ab^{2}c^3)^2*(-a^2b)^3=

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

Evaluate

$$-c^{6}b^{7}a^{8}$$

Solution Steps

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

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

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

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

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

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

Calculate -a to the power of 2 and get a^{2}.

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

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

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$a^{2}b^{7}c^{6}\left(-a^{2}\right)^{3}$$

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

$$a^{2}b^{7}c^{6}\left(-1\right)^{3}\left(a^{2}\right)^{3}$$

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

$$a^{2}b^{7}c^{6}\left(-1\right)^{3}a^{6}$$

Calculate -1 to the power of 3 and get -1.

$$a^{2}b^{7}c^{6}\left(-1\right)a^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$a^{8}b^{7}c^{6}\left(-1\right)$$

Expand

$$-c^{6}b^{7}a^{8}$$

Solution Steps

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

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

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

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

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

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

Calculate -a to the power of 2 and get a^{2}.

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

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

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$a^{2}b^{7}c^{6}\left(-a^{2}\right)^{3}$$

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

$$a^{2}b^{7}c^{6}\left(-1\right)^{3}\left(a^{2}\right)^{3}$$

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

$$a^{2}b^{7}c^{6}\left(-1\right)^{3}a^{6}$$

Calculate -1 to the power of 3 and get -1.

$$a^{2}b^{7}c^{6}\left(-1\right)a^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$a^{8}b^{7}c^{6}\left(-1\right)$$