Solve (-a^2)^4*(2a)^2div(-a)^7

$$( - a ^ { 2 } ) ^ { 4 } \cdot ( 2 a ) ^ { 2 } \div ( - a ) ^ { 7 }$$

Evaluate

$$-4a^{3}$$

Short Solution Steps

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

$$\frac{\left(-a^{2}\right)^{4}\times 2^{2}a^{2}}{\left(-a\right)^{7}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(-a^{2}\right)^{4}\times 4a^{2}}{\left(-a\right)^{7}}$$

Expand \left(-a^{2}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

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

Calculate -1 to the power of 4 and get 1.

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

Multiply 1 and 4 to get 4.

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

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{4a^{10}}{\left(-a\right)^{7}}$$

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

$$\frac{4a^{10}}{\left(-1\right)^{7}a^{7}}$$

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

$$\frac{4a^{10}}{-a^{7}}$$

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

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

Anything divided by -1 gives its opposite.

$$-4a^{3}$$

Expand

$$-4a^{3}$$

Short Solution Steps

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

$$\frac{\left(-a^{2}\right)^{4}\times 2^{2}a^{2}}{\left(-a\right)^{7}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(-a^{2}\right)^{4}\times 4a^{2}}{\left(-a\right)^{7}}$$

Expand \left(-a^{2}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

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

Calculate -1 to the power of 4 and get 1.

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

Multiply 1 and 4 to get 4.

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

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{4a^{10}}{\left(-a\right)^{7}}$$

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

$$\frac{4a^{10}}{\left(-1\right)^{7}a^{7}}$$

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

$$\frac{4a^{10}}{-a^{7}}$$

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

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

Anything divided by -1 gives its opposite.

$$-4a^{3}$$