Solve -a^{3}b^4*3abc^2*(a^3b)^2

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

Evaluate

$$-3c^{2}b^{7}a^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

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

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

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

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

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

$$\left(-a^{3}\right)b^{5}\times 3a^{7}c^{2}b^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

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

Multiply -1 and 3 to get -3.

$$-3a^{3}b^{7}a^{7}c^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$-3a^{10}b^{7}c^{2}$$

Expand

$$-3c^{2}b^{7}a^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

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

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

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

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

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

$$\left(-a^{3}\right)b^{5}\times 3a^{7}c^{2}b^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

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

Multiply -1 and 3 to get -3.

$$-3a^{3}b^{7}a^{7}c^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$-3a^{10}b^{7}c^{2}$$