Solve (-6a^2b^2c)^2div4ac^2=

$$( - 6 a ^ { 2 } b ^ { 2 } c ) ^ { 2 } \div 4 a c ^ { 2 } =$$

Evaluate

$$9a^{5}\left(bc\right)^{4}$$

Solution Steps

Expand \left(-6a^{2}b^{2}c\right)^{2}.

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

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

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

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

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

Calculate -6 to the power of 2 and get 36.

$$\frac{36a^{4}b^{4}c^{2}}{4}ac^{2}$$

Divide 36a^{4}b^{4}c^{2} by 4 to get 9a^{4}b^{4}c^{2}.

$$9a^{4}b^{4}c^{2}ac^{2}$$

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

$$9a^{5}b^{4}c^{2}c^{2}$$

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

$$9a^{5}b^{4}c^{4}$$

Expand

$$9a^{5}\left(bc\right)^{4}$$

Solution Steps

Expand \left(-6a^{2}b^{2}c\right)^{2}.

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

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

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

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

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

Calculate -6 to the power of 2 and get 36.

$$\frac{36a^{4}b^{4}c^{2}}{4}ac^{2}$$

Divide 36a^{4}b^{4}c^{2} by 4 to get 9a^{4}b^{4}c^{2}.

$$9a^{4}b^{4}c^{2}ac^{2}$$

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

$$9a^{5}b^{4}c^{2}c^{2}$$

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

$$9a^{5}b^{4}c^{4}$$