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

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

Evaluate

$$-\frac{a^{8}}{\left(bc\right)^{3}}$$

Short Solution Steps

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

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

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

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

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

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

To raise \frac{bc}{a} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

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

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

$$\frac{a^{10}b^{3}c^{4}}{\left(-c\right)^{3}\left(ab\right)^{2}\left(bc\right)^{4}}$$

Expand \left(ab\right)^{2}.

$$\frac{a^{10}b^{3}c^{4}}{\left(-c\right)^{3}a^{2}b^{2}\left(bc\right)^{4}}$$

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

$$\frac{a^{10}b^{3}c^{4}}{\left(-c\right)^{3}a^{2}b^{2}b^{4}c^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{a^{10}b^{3}c^{4}}{\left(-c\right)^{3}a^{2}b^{6}c^{4}}$$

Cancel out a^{2}b^{3}c^{4} in both numerator and denominator.

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

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

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

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

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

Expand

$$-\frac{a^{8}}{\left(bc\right)^{3}}$$

Short Solution Steps

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

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

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

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

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

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

To raise \frac{bc}{a} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

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

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

$$\frac{a^{10}b^{3}c^{4}}{\left(-c\right)^{3}\left(ab\right)^{2}\left(bc\right)^{4}}$$

Expand \left(ab\right)^{2}.

$$\frac{a^{10}b^{3}c^{4}}{\left(-c\right)^{3}a^{2}b^{2}\left(bc\right)^{4}}$$

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

$$\frac{a^{10}b^{3}c^{4}}{\left(-c\right)^{3}a^{2}b^{2}b^{4}c^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{a^{10}b^{3}c^{4}}{\left(-c\right)^{3}a^{2}b^{6}c^{4}}$$

Cancel out a^{2}b^{3}c^{4} in both numerator and denominator.

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

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

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

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

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