Solve (-1/4a^{3}b^{2})^{5}(-1/4a^{3}b^{2})^{2}(-1/4a^{3}b^2):(-1/4a^3b^2)^8

$$( - \frac { 1 } { 4 } a ^ { 3 } b ^ { 2 } ) ^ { 5 } ( - \frac { 1 } { 4 } a ^ { 3 } b ^ { 2 } ) ^ { 2 } ( - \frac { 1 } { 4 } a ^ { 3 } b ^ { 2 } ) : ( - \frac { 1 } { 4 } a ^ { 3 } b ^ { 2 } ) ^ { 8 }$$

Evaluate

$$1$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\left(-\frac{1}{4}a^{3}b^{2}\right)^{7}\left(-\frac{1}{4}\right)a^{3}b^{2}}{\left(-\frac{1}{4}a^{3}b^{2}\right)^{8}}$$

Cancel out \left(-\frac{1}{4}b^{2}a^{3}\right)^{7} in both numerator and denominator.

$$\frac{-\frac{1}{4}b^{2}a^{3}}{-\frac{1}{4}b^{2}a^{3}}$$

Cancel out b^{2}a^{3} in both numerator and denominator.

$$\frac{-\frac{1}{4}}{-\frac{1}{4}}$$

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

$$\frac{1}{\left(-\frac{1}{4}\right)^{0}}$$

Calculate -\frac{1}{4} to the power of 0 and get 1.

$$\frac{1}{1}$$

Anything divided by one gives itself.

$$1$$

Factor

$$1$$