Solve (-2a^2bc^3)^2div4abcd

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

Evaluate

$$db^{3}a^{5}c^{7}$$

Solution Steps

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

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

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

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

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

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

Calculate -2 to the power of 2 and get 4.

$$\frac{4a^{4}b^{2}c^{6}}{4}abcd$$

Cancel out 4 and 4.

$$a^{4}b^{2}c^{6}abcd$$

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

$$a^{5}b^{2}c^{6}bcd$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$a^{5}b^{3}c^{6}cd$$

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

$$a^{5}b^{3}c^{7}d$$

Expand

$$db^{3}a^{5}c^{7}$$

Solution Steps

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

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

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

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

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

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

Calculate -2 to the power of 2 and get 4.

$$\frac{4a^{4}b^{2}c^{6}}{4}abcd$$

Cancel out 4 and 4.

$$a^{4}b^{2}c^{6}abcd$$

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

$$a^{5}b^{2}c^{6}bcd$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$a^{5}b^{3}c^{6}cd$$

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

$$a^{5}b^{3}c^{7}d$$