Solve [(frac{a^{3}b^{-1}c^-2}{a^-2b^-2c})^-3]

$$[ ( \frac { a ^ { 3 } b ^ { - 1 } c ^ { - 2 } } { a ^ { - 2 } b ^ { - 2 } c } ) ^ { - 3 } ]$$

Evaluate

$$\frac{c^{9}}{b^{3}a^{15}}$$

Solution Steps

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

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

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

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

Calculate b to the power of 1 and get b.

$$\left(\frac{ba^{5}}{c^{3}}\right)^{-3}$$

To raise \frac{ba^{5}}{c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(ba^{5}\right)^{-3}}{\left(c^{3}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\left(ba^{5}\right)^{-3}}{c^{-9}}$$

Expand \left(ba^{5}\right)^{-3}.

$$\frac{b^{-3}\left(a^{5}\right)^{-3}}{c^{-9}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{b^{-3}a^{-15}}{c^{-9}}$$

Expand

$$\frac{c^{9}}{b^{3}a^{15}}$$

Solution Steps

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

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

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

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

Calculate b to the power of 1 and get b.

$$\left(\frac{ba^{5}}{c^{3}}\right)^{-3}$$

To raise \frac{ba^{5}}{c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(ba^{5}\right)^{-3}}{\left(c^{3}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\left(ba^{5}\right)^{-3}}{c^{-9}}$$

Expand \left(ba^{5}\right)^{-3}.

$$\frac{b^{-3}\left(a^{5}\right)^{-3}}{c^{-9}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{b^{-3}a^{-15}}{c^{-9}}$$