Solve (4x^2)^5/64x^12

$$\frac { ( 4 x ^ { 2 } ) ^ { 5 } } { 64 x ^ { 12 } }$$

Evaluate

$$\frac{16}{x^{2}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4x^{2}\right)^{5}\times \frac{1}{64x^{12}}$$

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

$$4^{5}\left(x^{2}\right)^{5}\times \frac{1}{64}\times \frac{1}{x^{12}}$$

Use the Commutative Property of Multiplication.

$$4^{5}\times \frac{1}{64}\left(x^{2}\right)^{5}\times \frac{1}{x^{12}}$$

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

$$4^{5}\times \frac{1}{64}x^{2\times 5}x^{12\left(-1\right)}$$

Multiply 2 times 5.

$$4^{5}\times \frac{1}{64}x^{10}x^{12\left(-1\right)}$$

Multiply 12 times -1.

$$4^{5}\times \frac{1}{64}x^{10}x^{-12}$$

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

$$4^{5}\times \frac{1}{64}x^{10-12}$$

Add the exponents 10 and -12.

$$4^{5}\times \frac{1}{64}x^{-2}$$

Raise 4 to the power 5.

$$1024\times \frac{1}{64}x^{-2}$$

Multiply 1024 times \frac{1}{64}.

$$16x^{-2}$$

Expand

$$\frac{16}{x^{2}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4x^{2}\right)^{5}\times \frac{1}{64x^{12}}$$

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

$$4^{5}\left(x^{2}\right)^{5}\times \frac{1}{64}\times \frac{1}{x^{12}}$$

Use the Commutative Property of Multiplication.

$$4^{5}\times \frac{1}{64}\left(x^{2}\right)^{5}\times \frac{1}{x^{12}}$$

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

$$4^{5}\times \frac{1}{64}x^{2\times 5}x^{12\left(-1\right)}$$

Multiply 2 times 5.

$$4^{5}\times \frac{1}{64}x^{10}x^{12\left(-1\right)}$$

Multiply 12 times -1.

$$4^{5}\times \frac{1}{64}x^{10}x^{-12}$$

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

$$4^{5}\times \frac{1}{64}x^{10-12}$$

Add the exponents 10 and -12.

$$4^{5}\times \frac{1}{64}x^{-2}$$

Raise 4 to the power 5.

$$1024\times \frac{1}{64}x^{-2}$$

Multiply 1024 times \frac{1}{64}.

$$16x^{-2}$$