Solve +1/2a^9:(-1/2a)^2

$$+ \frac { 1 } { 2 } a ^ { 9 } : ( - \frac { 1 } { 2 } a ) ^ { 2 }$$

Evaluate

$$2a^{7}$$

Solution Steps

Expand \left(-\frac{1}{2}a\right)^{2}.

$$\frac{\frac{1}{2}a^{9}}{\left(-\frac{1}{2}\right)^{2}a^{2}}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\frac{1}{2}a^{9}}{\frac{1}{4}a^{2}}$$

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

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

Divide \frac{1}{2}a^{7} by \frac{1}{4} by multiplying \frac{1}{2}a^{7} by the reciprocal of \frac{1}{4}.

$$\frac{1}{2}a^{7}\times 4$$

Multiply \frac{1}{2} and 4 to get 2.

$$2a^{7}$$

Expand

$$2a^{7}$$

Solution Steps

Expand \left(-\frac{1}{2}a\right)^{2}.

$$\frac{\frac{1}{2}a^{9}}{\left(-\frac{1}{2}\right)^{2}a^{2}}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\frac{1}{2}a^{9}}{\frac{1}{4}a^{2}}$$

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

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

Divide \frac{1}{2}a^{7} by \frac{1}{4} by multiplying \frac{1}{2}a^{7} by the reciprocal of \frac{1}{4}.

$$\frac{1}{2}a^{7}\times 4$$

Multiply \frac{1}{2} and 4 to get 2.

$$2a^{7}$$