Solve a^6diva^2quad(2)(-b)^8div(-b)

$$a ^ { 6 } \div a ^ { 2 } \quad ( 2 ) ( - b ) ^ { 8 } \div ( - b )$$

Evaluate

$$-2a^{4}b^{7}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 6 to get 4.

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

Expand \left(-b\right)^{8}.

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

Calculate -1 to the power of 8 and get 1.

$$\frac{a^{4}\times 2\times 1b^{8}}{-b}$$

Multiply 2 and 1 to get 2.

$$\frac{a^{4}\times 2b^{8}}{-b}$$

Cancel out b in both numerator and denominator.

$$\frac{2a^{4}b^{7}}{-1}$$

Anything divided by -1 gives its opposite.

$$-2a^{4}b^{7}$$

Expand

$$-2a^{4}b^{7}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 6 to get 4.

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

Expand \left(-b\right)^{8}.

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

Calculate -1 to the power of 8 and get 1.

$$\frac{a^{4}\times 2\times 1b^{8}}{-b}$$

Multiply 2 and 1 to get 2.

$$\frac{a^{4}\times 2b^{8}}{-b}$$

Cancel out b in both numerator and denominator.

$$\frac{2a^{4}b^{7}}{-1}$$

Anything divided by -1 gives its opposite.

$$-2a^{4}b^{7}$$