Solve ac^7/bdiv(a^5c/b)^2

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

Evaluate

$$\frac{bc^{5}}{a^{9}}$$

Solution Steps

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

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

Divide \frac{ac^{7}}{b} by \frac{\left(a^{5}c\right)^{2}}{b^{2}} by multiplying \frac{ac^{7}}{b} by the reciprocal of \frac{\left(a^{5}c\right)^{2}}{b^{2}}.

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

Cancel out b in both numerator and denominator.

$$\frac{abc^{7}}{\left(ca^{5}\right)^{2}}$$

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

$$\frac{abc^{7}}{c^{2}\left(a^{5}\right)^{2}}$$

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

$$\frac{abc^{7}}{c^{2}a^{10}}$$

Cancel out ac^{2} in both numerator and denominator.

$$\frac{bc^{5}}{a^{9}}$$

Expand

$$\frac{bc^{5}}{a^{9}}$$

Solution Steps

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

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

Divide \frac{ac^{7}}{b} by \frac{\left(a^{5}c\right)^{2}}{b^{2}} by multiplying \frac{ac^{7}}{b} by the reciprocal of \frac{\left(a^{5}c\right)^{2}}{b^{2}}.

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

Cancel out b in both numerator and denominator.

$$\frac{abc^{7}}{\left(ca^{5}\right)^{2}}$$

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

$$\frac{abc^{7}}{c^{2}\left(a^{5}\right)^{2}}$$

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

$$\frac{abc^{7}}{c^{2}a^{10}}$$

Cancel out ac^{2} in both numerator and denominator.

$$\frac{bc^{5}}{a^{9}}$$