Solve (5x^3)^2/25x^6

$$\frac { ( 5 x ^ { 3 } ) ^ { 2 } } { 25 x ^ { 6 } }$$

Evaluate

$$1$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(5x^{3}\right)^{2}\times \frac{1}{25x^{6}}$$

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

$$5^{2}\left(x^{3}\right)^{2}\times \frac{1}{25}\times \frac{1}{x^{6}}$$

Use the Commutative Property of Multiplication.

$$5^{2}\times \frac{1}{25}\left(x^{3}\right)^{2}\times \frac{1}{x^{6}}$$

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

$$5^{2}\times \frac{1}{25}x^{3\times 2}x^{6\left(-1\right)}$$

Multiply 3 times 2.

$$5^{2}\times \frac{1}{25}x^{6}x^{6\left(-1\right)}$$

Multiply 6 times -1.

$$5^{2}\times \frac{1}{25}x^{6}x^{-6}$$

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

$$5^{2}\times \frac{1}{25}x^{6-6}$$

Add the exponents 6 and -6.

$$5^{2}\times \frac{1}{25}x^{0}$$

Raise 5 to the power 2.

$$25\times \frac{1}{25}x^{0}$$

Multiply 25 times \frac{1}{25}.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$

Factor

$$1$$