Solve (-6a^{12}b^{7}z^{4}):(-2a^{9}b^{5}z^{3})^2*(-3/4ab^2z^3)^2

$$( - 6 a ^ { 12 } b ^ { 7 } z ^ { 4 } ) : ( - 2 a ^ { 9 } b ^ { 5 } z ^ { 3 } ) ^ { 2 } \cdot ( - \frac { 3 } { 4 } a b ^ { 2 } z ^ { 3 } ) ^ { 2 }$$

Evaluate

$$-\frac{27\times \left(\frac{z}{a}\right)^{4}b}{32}$$

Solution Steps

Expand \left(-2a^{9}b^{5}z^{3}\right)^{2}.

$$\frac{-6a^{12}b^{7}z^{4}}{\left(-2\right)^{2}\left(a^{9}\right)^{2}\left(b^{5}\right)^{2}\left(z^{3}\right)^{2}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\frac{-6a^{12}b^{7}z^{4}}{\left(-2\right)^{2}a^{18}\left(b^{5}\right)^{2}\left(z^{3}\right)^{2}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

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

$$\frac{-6a^{12}b^{7}z^{4}}{\left(-2\right)^{2}a^{18}b^{10}\left(z^{3}\right)^{2}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

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

$$\frac{-6a^{12}b^{7}z^{4}}{\left(-2\right)^{2}a^{18}b^{10}z^{6}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

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

$$\frac{-6a^{12}b^{7}z^{4}}{4a^{18}b^{10}z^{6}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

Cancel out 2z^{4}b^{7}a^{12} in both numerator and denominator.

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

Expand \left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}.

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

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

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

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

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

Calculate -\frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{-3}{2z^{2}b^{3}a^{6}}\times \frac{9}{16}a^{2}b^{4}z^{6}$$

Multiply \frac{-3}{2z^{2}b^{3}a^{6}} times \frac{9}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 9}{2z^{2}b^{3}a^{6}\times 16}a^{2}b^{4}z^{6}$$

Express \frac{-3\times 9}{2z^{2}b^{3}a^{6}\times 16}a^{2} as a single fraction.

$$\frac{-3\times 9a^{2}}{2z^{2}b^{3}a^{6}\times 16}b^{4}z^{6}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{-3\times 9}{2\times 16z^{2}b^{3}a^{4}}b^{4}z^{6}$$

Express \frac{-3\times 9}{2\times 16z^{2}b^{3}a^{4}}b^{4} as a single fraction.

$$\frac{-3\times 9b^{4}}{2\times 16z^{2}b^{3}a^{4}}z^{6}$$

Cancel out b^{3} in both numerator and denominator.

$$\frac{-3\times 9b}{2\times 16z^{2}a^{4}}z^{6}$$

Express \frac{-3\times 9b}{2\times 16z^{2}a^{4}}z^{6} as a single fraction.

$$\frac{-3\times 9bz^{6}}{2\times 16z^{2}a^{4}}$$

Cancel out z^{2} in both numerator and denominator.

$$\frac{-3\times 9bz^{4}}{2\times 16a^{4}}$$

Multiply -3 and 9 to get -27.

$$\frac{-27bz^{4}}{2\times 16a^{4}}$$

Multiply 2 and 16 to get 32.

$$\frac{-27bz^{4}}{32a^{4}}$$

Expand

$$-\frac{27\times \left(\frac{z}{a}\right)^{4}b}{32}$$

Solution Steps

Expand \left(-2a^{9}b^{5}z^{3}\right)^{2}.

$$\frac{-6a^{12}b^{7}z^{4}}{\left(-2\right)^{2}\left(a^{9}\right)^{2}\left(b^{5}\right)^{2}\left(z^{3}\right)^{2}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\frac{-6a^{12}b^{7}z^{4}}{\left(-2\right)^{2}a^{18}\left(b^{5}\right)^{2}\left(z^{3}\right)^{2}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

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

$$\frac{-6a^{12}b^{7}z^{4}}{\left(-2\right)^{2}a^{18}b^{10}\left(z^{3}\right)^{2}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

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

$$\frac{-6a^{12}b^{7}z^{4}}{\left(-2\right)^{2}a^{18}b^{10}z^{6}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

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

$$\frac{-6a^{12}b^{7}z^{4}}{4a^{18}b^{10}z^{6}}\left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}$$

Cancel out 2z^{4}b^{7}a^{12} in both numerator and denominator.

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

Expand \left(-\frac{3}{4}ab^{2}z^{3}\right)^{2}.

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

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

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

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

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

Calculate -\frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{-3}{2z^{2}b^{3}a^{6}}\times \frac{9}{16}a^{2}b^{4}z^{6}$$

Multiply \frac{-3}{2z^{2}b^{3}a^{6}} times \frac{9}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 9}{2z^{2}b^{3}a^{6}\times 16}a^{2}b^{4}z^{6}$$

Express \frac{-3\times 9}{2z^{2}b^{3}a^{6}\times 16}a^{2} as a single fraction.

$$\frac{-3\times 9a^{2}}{2z^{2}b^{3}a^{6}\times 16}b^{4}z^{6}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{-3\times 9}{2\times 16z^{2}b^{3}a^{4}}b^{4}z^{6}$$

Express \frac{-3\times 9}{2\times 16z^{2}b^{3}a^{4}}b^{4} as a single fraction.

$$\frac{-3\times 9b^{4}}{2\times 16z^{2}b^{3}a^{4}}z^{6}$$

Cancel out b^{3} in both numerator and denominator.

$$\frac{-3\times 9b}{2\times 16z^{2}a^{4}}z^{6}$$

Express \frac{-3\times 9b}{2\times 16z^{2}a^{4}}z^{6} as a single fraction.

$$\frac{-3\times 9bz^{6}}{2\times 16z^{2}a^{4}}$$

Cancel out z^{2} in both numerator and denominator.

$$\frac{-3\times 9bz^{4}}{2\times 16a^{4}}$$

Multiply -3 and 9 to get -27.

$$\frac{-27bz^{4}}{2\times 16a^{4}}$$

Multiply 2 and 16 to get 32.

$$\frac{-27bz^{4}}{32a^{4}}$$