Solve (2x^4)^3/x^15

$$\frac { ( 2 x ^ { 4 } ) ^ { 3 } } { x ^ { 15 } }$$

Evaluate

$$\frac{8}{x^{3}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2x^{4}\right)^{3}\times \frac{1}{x^{15}}$$

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

$$2^{3}\left(x^{4}\right)^{3}\times \frac{1}{1}\times \frac{1}{x^{15}}$$

Use the Commutative Property of Multiplication.

$$2^{3}\times \frac{1}{1}\left(x^{4}\right)^{3}\times \frac{1}{x^{15}}$$

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

$$2^{3}\times \frac{1}{1}x^{4\times 3}x^{15\left(-1\right)}$$

Multiply 4 times 3.

$$2^{3}\times \frac{1}{1}x^{12}x^{15\left(-1\right)}$$

Multiply 15 times -1.

$$2^{3}\times \frac{1}{1}x^{12}x^{-15}$$

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

$$2^{3}\times \frac{1}{1}x^{12-15}$$

Add the exponents 12 and -15.

$$2^{3}\times \frac{1}{1}x^{-3}$$

Raise 2 to the power 3.

$$8\times \frac{1}{1}x^{-3}$$

Expand

$$\frac{8}{x^{3}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2x^{4}\right)^{3}\times \frac{1}{x^{15}}$$

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

$$2^{3}\left(x^{4}\right)^{3}\times \frac{1}{1}\times \frac{1}{x^{15}}$$

Use the Commutative Property of Multiplication.

$$2^{3}\times \frac{1}{1}\left(x^{4}\right)^{3}\times \frac{1}{x^{15}}$$

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

$$2^{3}\times \frac{1}{1}x^{4\times 3}x^{15\left(-1\right)}$$

Multiply 4 times 3.

$$2^{3}\times \frac{1}{1}x^{12}x^{15\left(-1\right)}$$

Multiply 15 times -1.

$$2^{3}\times \frac{1}{1}x^{12}x^{-15}$$

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

$$2^{3}\times \frac{1}{1}x^{12-15}$$

Add the exponents 12 and -15.

$$2^{3}\times \frac{1}{1}x^{-3}$$

Raise 2 to the power 3.

$$8\times \frac{1}{1}x^{-3}$$