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

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

Evaluate

$$\frac{1}{32x^{4}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times -3.

$$2^{-3}\times \frac{1}{4}x^{-6}x^{-2\left(-1\right)}$$

Multiply -2 times -1.

$$2^{-3}\times \frac{1}{4}x^{-6}x^{2}$$

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

$$2^{-3}\times \frac{1}{4}x^{-6+2}$$

Add the exponents -6 and 2.

$$2^{-3}\times \frac{1}{4}x^{-4}$$

Raise 2 to the power -3.

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

Multiply \frac{1}{8} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{32}x^{-4}$$

Expand

$$\frac{1}{32x^{4}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times -3.

$$2^{-3}\times \frac{1}{4}x^{-6}x^{-2\left(-1\right)}$$

Multiply -2 times -1.

$$2^{-3}\times \frac{1}{4}x^{-6}x^{2}$$

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

$$2^{-3}\times \frac{1}{4}x^{-6+2}$$

Add the exponents -6 and 2.

$$2^{-3}\times \frac{1}{4}x^{-4}$$

Raise 2 to the power -3.

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

Multiply \frac{1}{8} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{32}x^{-4}$$