Answer :
- Multiply the coefficients: $4 \times 2 = 8$.
- Add the exponents of $x$: $x^3 \times x^3 = x^{3+3} = x^6$.
- Combine the results: $8x^6$.
- The simplified expression is $\boxed{8x^6}$.
### Explanation
1. Understanding the problem
We are asked to simplify the expression $4x^3 \times 2x^3$. This involves multiplying the coefficients and adding the exponents of the variable $x$.
2. Multiplying the coefficients
First, we multiply the coefficients: $4 \times 2 = 8$.
3. Multiplying the variables with exponents
Next, we multiply the variables with exponents: $x^3 \times x^3 = x^{3+3} = x^6$. Remember that when multiplying terms with the same base, you add the exponents.
4. Combining the results
Finally, we combine the results: $8x^6$. Therefore, the simplified expression is $8x^6$.
### Examples
Understanding how to simplify expressions with exponents is useful in many areas, such as calculating the area or volume of geometric shapes. For example, if you have a cube with side length $2x^3$, its volume would be $(2x^3)^3 = 8x^9$. Simplifying expressions also helps in physics, such as when dealing with quantities that scale with powers of a variable.
- Add the exponents of $x$: $x^3 \times x^3 = x^{3+3} = x^6$.
- Combine the results: $8x^6$.
- The simplified expression is $\boxed{8x^6}$.
### Explanation
1. Understanding the problem
We are asked to simplify the expression $4x^3 \times 2x^3$. This involves multiplying the coefficients and adding the exponents of the variable $x$.
2. Multiplying the coefficients
First, we multiply the coefficients: $4 \times 2 = 8$.
3. Multiplying the variables with exponents
Next, we multiply the variables with exponents: $x^3 \times x^3 = x^{3+3} = x^6$. Remember that when multiplying terms with the same base, you add the exponents.
4. Combining the results
Finally, we combine the results: $8x^6$. Therefore, the simplified expression is $8x^6$.
### Examples
Understanding how to simplify expressions with exponents is useful in many areas, such as calculating the area or volume of geometric shapes. For example, if you have a cube with side length $2x^3$, its volume would be $(2x^3)^3 = 8x^9$. Simplifying expressions also helps in physics, such as when dealing with quantities that scale with powers of a variable.
