Solve (5x^2)^3/5x^4

$$\frac { ( 5 x ^ { 2 } ) ^ { 3 } } { 5 x ^ { 4 } }$$

Evaluate

$$25x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(5x^{2}\right)^{3}\times \frac{1}{5x^{4}}$$

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

$$5^{3}\left(x^{2}\right)^{3}\times \frac{1}{5}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$5^{3}\times \frac{1}{5}\left(x^{2}\right)^{3}\times \frac{1}{x^{4}}$$

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

$$5^{3}\times \frac{1}{5}x^{2\times 3}x^{4\left(-1\right)}$$

Multiply 2 times 3.

$$5^{3}\times \frac{1}{5}x^{6}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$5^{3}\times \frac{1}{5}x^{6}x^{-4}$$

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

$$5^{3}\times \frac{1}{5}x^{6-4}$$

Add the exponents 6 and -4.

$$5^{3}\times \frac{1}{5}x^{2}$$

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

$$5^{3-1}x^{2}$$

Add the exponents 3 and -1.

$$5^{2}x^{2}$$

Expand

$$25x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(5x^{2}\right)^{3}\times \frac{1}{5x^{4}}$$

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

$$5^{3}\left(x^{2}\right)^{3}\times \frac{1}{5}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$5^{3}\times \frac{1}{5}\left(x^{2}\right)^{3}\times \frac{1}{x^{4}}$$

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

$$5^{3}\times \frac{1}{5}x^{2\times 3}x^{4\left(-1\right)}$$

Multiply 2 times 3.

$$5^{3}\times \frac{1}{5}x^{6}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$5^{3}\times \frac{1}{5}x^{6}x^{-4}$$

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

$$5^{3}\times \frac{1}{5}x^{6-4}$$

Add the exponents 6 and -4.

$$5^{3}\times \frac{1}{5}x^{2}$$

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

$$5^{3-1}x^{2}$$

Add the exponents 3 and -1.

$$5^{2}x^{2}$$