Solve (frac{a^{-3}b^{-2}c}{a^-5b^-7c^3})^-2

$$( \frac { a ^ { - 3 } b ^ { - 2 } c } { a ^ { - 5 } b ^ { - 7 } c ^ { 3 } } ) ^ { - 2 }$$

Evaluate

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

Solution Steps

Cancel out c in both numerator and denominator.

$$\left(\frac{a^{-3}b^{-2}}{b^{-7}a^{-5}c^{2}}\right)^{-2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To raise \frac{a^{2}b^{5}}{c^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

$$\frac{a^{-4}b^{-10}}{c^{-4}}$$

Expand

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

Solution Steps

Cancel out c in both numerator and denominator.

$$\left(\frac{a^{-3}b^{-2}}{b^{-7}a^{-5}c^{2}}\right)^{-2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To raise \frac{a^{2}b^{5}}{c^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

$$\frac{a^{-4}b^{-10}}{c^{-4}}$$