Solve -a^8{left(-b/aright)}^7{left(-1/bright)}^6

$$- { a }^{ 8 } { \left(- \frac{ b }{ a } \right) }^{ 7 } { \left(- \frac{ 1 }{ b } \right) }^{ 6 }$$

Evaluate

$$ab$$

Solution Steps

Expand \left(-\frac{b}{a}\right)^{7}.

$$-a^{8}\left(-1\right)^{7}\times \left(\frac{b}{a}\right)^{7}\left(-\frac{1}{b}\right)^{6}$$

Calculate -1 to the power of 7 and get -1.

$$-a^{8}\left(-1\right)\times \left(\frac{b}{a}\right)^{7}\left(-\frac{1}{b}\right)^{6}$$

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

$$-a^{8}\left(-1\right)\times \frac{b^{7}}{a^{7}}\left(-\frac{1}{b}\right)^{6}$$

Multiply -1 and -1 to get 1.

$$a^{8}\times \frac{b^{7}}{a^{7}}\left(-\frac{1}{b}\right)^{6}$$

Expand \left(-\frac{1}{b}\right)^{6}.

$$a^{8}\times \frac{b^{7}}{a^{7}}\left(-1\right)^{6}\times \left(\frac{1}{b}\right)^{6}$$

Calculate -1 to the power of 6 and get 1.

$$a^{8}\times \frac{b^{7}}{a^{7}}\times 1\times \left(\frac{1}{b}\right)^{6}$$

To raise \frac{1}{b} to a power, raise both numerator and denominator to the power and then divide.

$$a^{8}\times \frac{b^{7}}{a^{7}}\times 1\times \frac{1^{6}}{b^{6}}$$

Express 1\times \frac{1^{6}}{b^{6}} as a single fraction.

$$a^{8}\times \frac{b^{7}}{a^{7}}\times \frac{1^{6}}{b^{6}}$$

Express a^{8}\times \frac{b^{7}}{a^{7}} as a single fraction.

$$\frac{a^{8}b^{7}}{a^{7}}\times \frac{1^{6}}{b^{6}}$$

Cancel out a^{7} in both numerator and denominator.

$$ab^{7}\times \frac{1^{6}}{b^{6}}$$

Express ab^{7}\times \frac{1^{6}}{b^{6}} as a single fraction.

$$\frac{ab^{7}\times 1^{6}}{b^{6}}$$

Cancel out b^{6} in both numerator and denominator.

$$1^{6}ab$$

Calculate 1 to the power of 6 and get 1.

$$1ab$$

For any term t, t\times 1=t and 1t=t.

$$ab$$

Expand

$$ab$$

Solution Steps

Expand \left(-\frac{b}{a}\right)^{7}.

$$-a^{8}\left(-1\right)^{7}\times \left(\frac{b}{a}\right)^{7}\left(-\frac{1}{b}\right)^{6}$$

Calculate -1 to the power of 7 and get -1.

$$-a^{8}\left(-1\right)\times \left(\frac{b}{a}\right)^{7}\left(-\frac{1}{b}\right)^{6}$$

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

$$-a^{8}\left(-1\right)\times \frac{b^{7}}{a^{7}}\left(-\frac{1}{b}\right)^{6}$$

Multiply -1 and -1 to get 1.

$$a^{8}\times \frac{b^{7}}{a^{7}}\left(-\frac{1}{b}\right)^{6}$$

Expand \left(-\frac{1}{b}\right)^{6}.

$$a^{8}\times \frac{b^{7}}{a^{7}}\left(-1\right)^{6}\times \left(\frac{1}{b}\right)^{6}$$

Calculate -1 to the power of 6 and get 1.

$$a^{8}\times \frac{b^{7}}{a^{7}}\times 1\times \left(\frac{1}{b}\right)^{6}$$

To raise \frac{1}{b} to a power, raise both numerator and denominator to the power and then divide.

$$a^{8}\times \frac{b^{7}}{a^{7}}\times 1\times \frac{1^{6}}{b^{6}}$$

Express 1\times \frac{1^{6}}{b^{6}} as a single fraction.

$$a^{8}\times \frac{b^{7}}{a^{7}}\times \frac{1^{6}}{b^{6}}$$

Express a^{8}\times \frac{b^{7}}{a^{7}} as a single fraction.

$$\frac{a^{8}b^{7}}{a^{7}}\times \frac{1^{6}}{b^{6}}$$

Cancel out a^{7} in both numerator and denominator.

$$ab^{7}\times \frac{1^{6}}{b^{6}}$$

Express ab^{7}\times \frac{1^{6}}{b^{6}} as a single fraction.

$$\frac{ab^{7}\times 1^{6}}{b^{6}}$$

Cancel out b^{6} in both numerator and denominator.

$$1^{6}ab$$

Calculate 1 to the power of 6 and get 1.

$$1ab$$

For any term t, t\times 1=t and 1t=t.

$$ab$$