Solve (frac{5a^{-4}b^{5}c^{2}}{25a^-4b^6c^-1})^-2

$$( \frac { 5 a ^ { - 4 } b ^ { 5 } c ^ { 2 } } { 25 a ^ { - 4 } b ^ { 6 } c ^ { - 1 } } ) ^ { - 2 }$$

Evaluate

$$\frac{25b^{2}}{c^{6}}$$

Solution Steps

Cancel out 5a^{-4}b^{5} in both numerator and denominator.

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

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

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

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

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

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

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

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

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

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{c^{-6}}{\frac{1}{25}b^{-2}}$$

Expand

$$\frac{25b^{2}}{c^{6}}$$

Solution Steps

Cancel out 5a^{-4}b^{5} in both numerator and denominator.

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

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

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

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

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

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

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

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

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

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{c^{-6}}{\frac{1}{25}b^{-2}}$$