Solve x^3left(5x^3right)^3

$${ x }^{ 3 } { \left(5 { x }^{ 3 } \right) }^{ 3 }$$

Evaluate

$$125x^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 3 times 3.

$$1^{3}\times 5^{3}x^{3}x^{9}$$

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

$$1^{3}\times 5^{3}x^{3+9}$$

Add the exponents 3 and 9.

$$1^{3}\times 5^{3}x^{12}$$

Raise 5 to the power 3.

$$125x^{12}$$

Expand

$$125x^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 3 times 3.

$$1^{3}\times 5^{3}x^{3}x^{9}$$

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

$$1^{3}\times 5^{3}x^{3+9}$$

Add the exponents 3 and 9.

$$1^{3}\times 5^{3}x^{12}$$

Raise 5 to the power 3.

$$125x^{12}$$