Solve (-2a^2)^3diva^2

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

Evaluate

$$-8a^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply 2 times 3.

$$\left(-2\right)^{3}\times \frac{1}{1}a^{6}a^{2\left(-1\right)}$$

Multiply 2 times -1.

$$\left(-2\right)^{3}\times \frac{1}{1}a^{6}a^{-2}$$

To multiply powers of the same base, add their exponents.

$$\left(-2\right)^{3}\times \frac{1}{1}a^{6-2}$$

Add the exponents 6 and -2.

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

Raise -2 to the power 3.

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

Expand

$$-8a^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply 2 times 3.

$$\left(-2\right)^{3}\times \frac{1}{1}a^{6}a^{2\left(-1\right)}$$

Multiply 2 times -1.

$$\left(-2\right)^{3}\times \frac{1}{1}a^{6}a^{-2}$$

To multiply powers of the same base, add their exponents.

$$\left(-2\right)^{3}\times \frac{1}{1}a^{6-2}$$

Add the exponents 6 and -2.

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

Raise -2 to the power 3.

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