Solve left(-8x^3right)^2left(8x^4right)^-1

$${ \left(-8 { x }^{ 3 } \right) }^{ 2 } { \left(8 { x }^{ 4 } \right) }^{ -1 }$$

Evaluate

$$8x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-8x^{3}\right)^{2}\times \frac{1}{8x^{4}}$$

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

$$\left(-8\right)^{2}\left(x^{3}\right)^{2}\times \frac{1}{8}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$\left(-8\right)^{2}\times \frac{1}{8}\left(x^{3}\right)^{2}\times \frac{1}{x^{4}}$$

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

$$\left(-8\right)^{2}\times \frac{1}{8}x^{3\times 2}x^{4\left(-1\right)}$$

Multiply 3 times 2.

$$\left(-8\right)^{2}\times \frac{1}{8}x^{6}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$\left(-8\right)^{2}\times \frac{1}{8}x^{6}x^{-4}$$

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

$$\left(-8\right)^{2}\times \frac{1}{8}x^{6-4}$$

Add the exponents 6 and -4.

$$\left(-8\right)^{2}\times \frac{1}{8}x^{2}$$

Raise -8 to the power 2.

$$64\times \frac{1}{8}x^{2}$$

Multiply 64 times \frac{1}{8}.

$$8x^{2}$$

Expand

$$8x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-8x^{3}\right)^{2}\times \frac{1}{8x^{4}}$$

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

$$\left(-8\right)^{2}\left(x^{3}\right)^{2}\times \frac{1}{8}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$\left(-8\right)^{2}\times \frac{1}{8}\left(x^{3}\right)^{2}\times \frac{1}{x^{4}}$$

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

$$\left(-8\right)^{2}\times \frac{1}{8}x^{3\times 2}x^{4\left(-1\right)}$$

Multiply 3 times 2.

$$\left(-8\right)^{2}\times \frac{1}{8}x^{6}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$\left(-8\right)^{2}\times \frac{1}{8}x^{6}x^{-4}$$

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

$$\left(-8\right)^{2}\times \frac{1}{8}x^{6-4}$$

Add the exponents 6 and -4.

$$\left(-8\right)^{2}\times \frac{1}{8}x^{2}$$

Raise -8 to the power 2.

$$64\times \frac{1}{8}x^{2}$$

Multiply 64 times \frac{1}{8}.

$$8x^{2}$$