Solve left(-2a^3right)^4divleft(a^2right)^3/{a^6}

$${ \left(-2 { a }^{ 3 } \right) }^{ 4 } \div \frac{ { \left( { a }^{ 2 } \right) }^{ 3 } }{ { a }^{ 6 } }$$

Evaluate

$$16a^{12}$$

Solution Steps

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

$$\frac{\left(-2a^{3}\right)^{4}}{\frac{a^{6}}{a^{6}}}$$

Divide a^{6} by a^{6} to get 1.

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

Expand \left(-2a^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(-2\right)^{4}a^{12}}{1}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{16a^{12}}{1}$$

Anything divided by one gives itself.

$$16a^{12}$$

Expand

$$16a^{12}$$

Solution Steps

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

$$\frac{\left(-2a^{3}\right)^{4}}{\frac{a^{6}}{a^{6}}}$$

Divide a^{6} by a^{6} to get 1.

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

Expand \left(-2a^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(-2\right)^{4}a^{12}}{1}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{16a^{12}}{1}$$

Anything divided by one gives itself.

$$16a^{12}$$