Solve (-a/b)^2div(2a^2/5b)^2*a/5b

$$( \frac { - a } { b } ) ^ { 2 } \div ( \frac { 2 a ^ { 2 } } { 5 b } ) ^ { 2 } \times \frac { a } { 5 b }$$

Evaluate

$$\frac{5}{4ab}$$

Short Solution Steps

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

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

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

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

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

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

Calculate -a to the power of 2 and get a^{2}.

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

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

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

Calculate 5 to the power of 2 and get 25.

$$\frac{a^{2}\times 25b^{2}}{b^{2}\times \left(2a^{2}\right)^{2}}\times \frac{a}{5b}$$

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

$$\frac{a^{2}\times 25b^{2}}{b^{2}\times 2^{2}\left(a^{2}\right)^{2}}\times \frac{a}{5b}$$

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

$$\frac{a^{2}\times 25b^{2}}{b^{2}\times 2^{2}a^{4}}\times \frac{a}{5b}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{a^{2}\times 25b^{2}}{b^{2}\times 4a^{4}}\times \frac{a}{5b}$$

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

$$\frac{25}{4a^{2}}\times \frac{a}{5b}$$

Multiply \frac{25}{4a^{2}} times \frac{a}{5b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25a}{4a^{2}\times 5b}$$

Cancel out 5a in both numerator and denominator.

$$\frac{5}{4ab}$$

Expand

$$\frac{5}{4ab}$$

Short Solution Steps

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

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

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

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

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

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

Calculate -a to the power of 2 and get a^{2}.

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

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

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

Calculate 5 to the power of 2 and get 25.

$$\frac{a^{2}\times 25b^{2}}{b^{2}\times \left(2a^{2}\right)^{2}}\times \frac{a}{5b}$$

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

$$\frac{a^{2}\times 25b^{2}}{b^{2}\times 2^{2}\left(a^{2}\right)^{2}}\times \frac{a}{5b}$$

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

$$\frac{a^{2}\times 25b^{2}}{b^{2}\times 2^{2}a^{4}}\times \frac{a}{5b}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{a^{2}\times 25b^{2}}{b^{2}\times 4a^{4}}\times \frac{a}{5b}$$

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

$$\frac{25}{4a^{2}}\times \frac{a}{5b}$$

Multiply \frac{25}{4a^{2}} times \frac{a}{5b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25a}{4a^{2}\times 5b}$$

Cancel out 5a in both numerator and denominator.

$$\frac{5}{4ab}$$