Solve (4p)^2/64p^4

$$\frac { ( 4 p ) ^ { 2 } } { 64 p ^ { 4 } }$$

Evaluate

$$\frac{1}{4p^{2}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4p^{1}\right)^{2}\times \frac{1}{64p^{4}}$$

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

$$4^{2}\left(p^{1}\right)^{2}\times \frac{1}{64}\times \frac{1}{p^{4}}$$

Use the Commutative Property of Multiplication.

$$4^{2}\times \frac{1}{64}\left(p^{1}\right)^{2}\times \frac{1}{p^{4}}$$

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

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

Multiply 4 times -1.

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

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

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

Add the exponents 2 and -4.

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

Raise 4 to the power 2.

$$16\times \frac{1}{64}p^{-2}$$

Multiply 16 times \frac{1}{64}.

$$\frac{1}{4}p^{-2}$$

Expand

$$\frac{1}{4p^{2}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4p^{1}\right)^{2}\times \frac{1}{64p^{4}}$$

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

$$4^{2}\left(p^{1}\right)^{2}\times \frac{1}{64}\times \frac{1}{p^{4}}$$

Use the Commutative Property of Multiplication.

$$4^{2}\times \frac{1}{64}\left(p^{1}\right)^{2}\times \frac{1}{p^{4}}$$

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

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

Multiply 4 times -1.

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

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

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

Add the exponents 2 and -4.

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

Raise 4 to the power 2.

$$16\times \frac{1}{64}p^{-2}$$

Multiply 16 times \frac{1}{64}.

$$\frac{1}{4}p^{-2}$$