Solve (frac{ac^{2}}{-b})^{3}*(b^2/ac)^4div(c^2b/-2a)^3

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

Evaluate

$$\frac{8\left(ab\right)^{2}}{c^{4}}$$

Short Solution Steps

To raise \frac{ac^{2}}{-b} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{b^{2}}{ac} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(ac^{2}\right)^{3}}{\left(-b\right)^{3}} times \frac{\left(b^{2}\right)^{4}}{\left(ac\right)^{4}} by multiplying numerator times numerator and denominator times denominator.

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

To raise \frac{c^{2}b}{-2a} to a power, raise both numerator and denominator to the power and then divide.

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

Divide \frac{\left(ac^{2}\right)^{3}\left(b^{2}\right)^{4}}{\left(-b\right)^{3}\left(ac\right)^{4}} by \frac{\left(c^{2}b\right)^{3}}{\left(-2a\right)^{3}} by multiplying \frac{\left(ac^{2}\right)^{3}\left(b^{2}\right)^{4}}{\left(-b\right)^{3}\left(ac\right)^{4}} by the reciprocal of \frac{\left(c^{2}b\right)^{3}}{\left(-2a\right)^{3}}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{\left(ac^{2}\right)^{3}b^{8}\left(-2a\right)^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

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

$$\frac{a^{3}\left(c^{2}\right)^{3}b^{8}\left(-2a\right)^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

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

$$\frac{a^{3}c^{6}b^{8}\left(-2a\right)^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

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

$$\frac{a^{3}c^{6}b^{8}\left(-2\right)^{3}a^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{a^{3}c^{6}b^{8}\left(-8\right)a^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

Expand \left(ac\right)^{4}.

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}a^{4}c^{4}\left(c^{2}b\right)^{3}}$$

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

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}a^{4}c^{4}\left(c^{2}\right)^{3}b^{3}}$$

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

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}a^{4}c^{4}c^{6}b^{3}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}a^{4}c^{10}b^{3}}$$

Cancel out b^{3}a^{4}c^{6} in both numerator and denominator.

$$\frac{-8a^{2}b^{5}}{\left(-b\right)^{3}c^{4}}$$

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

$$\frac{-8a^{2}b^{5}}{\left(-1\right)^{3}b^{3}c^{4}}$$

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

$$\frac{-8a^{2}b^{5}}{-b^{3}c^{4}}$$

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

$$\frac{-8a^{2}b^{2}}{-c^{4}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{8a^{2}b^{2}}{c^{4}}$$

Expand

$$\frac{8\left(ab\right)^{2}}{c^{4}}$$

Short Solution Steps

To raise \frac{ac^{2}}{-b} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{b^{2}}{ac} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(ac^{2}\right)^{3}}{\left(-b\right)^{3}} times \frac{\left(b^{2}\right)^{4}}{\left(ac\right)^{4}} by multiplying numerator times numerator and denominator times denominator.

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

To raise \frac{c^{2}b}{-2a} to a power, raise both numerator and denominator to the power and then divide.

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

Divide \frac{\left(ac^{2}\right)^{3}\left(b^{2}\right)^{4}}{\left(-b\right)^{3}\left(ac\right)^{4}} by \frac{\left(c^{2}b\right)^{3}}{\left(-2a\right)^{3}} by multiplying \frac{\left(ac^{2}\right)^{3}\left(b^{2}\right)^{4}}{\left(-b\right)^{3}\left(ac\right)^{4}} by the reciprocal of \frac{\left(c^{2}b\right)^{3}}{\left(-2a\right)^{3}}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{\left(ac^{2}\right)^{3}b^{8}\left(-2a\right)^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

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

$$\frac{a^{3}\left(c^{2}\right)^{3}b^{8}\left(-2a\right)^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

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

$$\frac{a^{3}c^{6}b^{8}\left(-2a\right)^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

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

$$\frac{a^{3}c^{6}b^{8}\left(-2\right)^{3}a^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{a^{3}c^{6}b^{8}\left(-8\right)a^{3}}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}\left(ac\right)^{4}\left(c^{2}b\right)^{3}}$$

Expand \left(ac\right)^{4}.

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}a^{4}c^{4}\left(c^{2}b\right)^{3}}$$

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

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}a^{4}c^{4}\left(c^{2}\right)^{3}b^{3}}$$

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

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}a^{4}c^{4}c^{6}b^{3}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{a^{6}c^{6}b^{8}\left(-8\right)}{\left(-b\right)^{3}a^{4}c^{10}b^{3}}$$

Cancel out b^{3}a^{4}c^{6} in both numerator and denominator.

$$\frac{-8a^{2}b^{5}}{\left(-b\right)^{3}c^{4}}$$

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

$$\frac{-8a^{2}b^{5}}{\left(-1\right)^{3}b^{3}c^{4}}$$

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

$$\frac{-8a^{2}b^{5}}{-b^{3}c^{4}}$$

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

$$\frac{-8a^{2}b^{2}}{-c^{4}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{8a^{2}b^{2}}{c^{4}}$$