Solve (a/a^-6b^5c)^-2

$$( \frac { a } { a ^ { - 6 } b ^ { 5 } c } ) ^ { - 2 }$$

Evaluate

$$\frac{c^{2}b^{10}}{a^{14}}$$

Solution Steps

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

$$\left(\frac{a^{7}}{cb^{5}}\right)^{-2}$$

To raise \frac{a^{7}}{cb^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{7}\right)^{-2}}{\left(cb^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{a^{-14}}{\left(cb^{5}\right)^{-2}}$$

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

$$\frac{a^{-14}}{c^{-2}\left(b^{5}\right)^{-2}}$$

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

$$\frac{a^{-14}}{c^{-2}b^{-10}}$$

Expand

$$\frac{c^{2}b^{10}}{a^{14}}$$

Solution Steps

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

$$\left(\frac{a^{7}}{cb^{5}}\right)^{-2}$$

To raise \frac{a^{7}}{cb^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{7}\right)^{-2}}{\left(cb^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{a^{-14}}{\left(cb^{5}\right)^{-2}}$$

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

$$\frac{a^{-14}}{c^{-2}\left(b^{5}\right)^{-2}}$$

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

$$\frac{a^{-14}}{c^{-2}b^{-10}}$$