Solve (-2a^{4})^2*(-a^3)div(-a^2)^3

$$( - 2 a ^ { 4 } ) ^ { 2 } \cdot ( - a ^ { 3 } ) \div ( - a ^ { 2 } ) ^ { 3 }$$

Evaluate

$$4a^{5}$$

Short Solution Steps

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

$$\frac{\left(-2\right)^{2}\left(a^{4}\right)^{2}\left(-a^{3}\right)}{\left(-a^{2}\right)^{3}}$$

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

$$\frac{\left(-2\right)^{2}a^{8}\left(-a^{3}\right)}{\left(-a^{2}\right)^{3}}$$

Calculate -2 to the power of 2 and get 4.

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

Multiply 4 and -1 to get -4.

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

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$\frac{-4a^{11}}{\left(-a^{2}\right)^{3}}$$

Expand \left(-a^{2}\right)^{3}.

$$\frac{-4a^{11}}{\left(-1\right)^{3}\left(a^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{-4a^{11}}{\left(-1\right)^{3}a^{6}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{-4a^{11}}{-a^{6}}$$

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

$$\frac{-4a^{5}}{-1}$$

Anything divided by -1 gives its opposite.

$$4a^{5}$$

Expand

$$4a^{5}$$

Short Solution Steps

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

$$\frac{\left(-2\right)^{2}\left(a^{4}\right)^{2}\left(-a^{3}\right)}{\left(-a^{2}\right)^{3}}$$

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

$$\frac{\left(-2\right)^{2}a^{8}\left(-a^{3}\right)}{\left(-a^{2}\right)^{3}}$$

Calculate -2 to the power of 2 and get 4.

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

Multiply 4 and -1 to get -4.

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

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$\frac{-4a^{11}}{\left(-a^{2}\right)^{3}}$$

Expand \left(-a^{2}\right)^{3}.

$$\frac{-4a^{11}}{\left(-1\right)^{3}\left(a^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{-4a^{11}}{\left(-1\right)^{3}a^{6}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{-4a^{11}}{-a^{6}}$$

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

$$\frac{-4a^{5}}{-1}$$

Anything divided by -1 gives its opposite.

$$4a^{5}$$