Answer :
- Rewrite the expression: $-x {imes} 4x^9 = -1 {imes} x^1 {imes} 4 {imes} x^9$.
- Group constants and variables: $(-1 {imes} 4) {imes} (x^1 {imes} x^9)$.
- Multiply constants: $-1 {imes} 4 = -4$.
- Multiply variables using exponent rules: $x^1 {imes} x^9 = x^{10}$.
- Combine to get the final answer: $\boxed{{-4x^{10}}}$.
### Explanation
1. Understanding the problem
We are asked to simplify the expression $-x {imes} 4x^9$. This involves multiplying a constant and variables with exponents. We will use the properties of exponents to simplify the expression.
2. Rewriting the expression
First, we rewrite the expression as $-1 {imes} x^1 {imes} 4 {imes} x^9$.
3. Rearranging terms
Next, we rearrange the terms to group the constants and the variables: $(-1 {imes} 4) {imes} (x^1 {imes} x^9)$.
4. Multiplying constants
Now, we multiply the constants: $-1 {imes} 4 = -4$.
5. Multiplying variables
We multiply the variables using the exponent rule $x^a {imes} x^b = x^{a+b}$: $x^1 {imes} x^9 = x^{1+9} = x^{10}$.
6. Combining the results
Finally, we combine the results to get the simplified expression: $-4x^{10}$.
### 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 square with side length $2x^3$, its area is $(2x^3)^2 = 4x^6$. Simplifying expressions helps in physics when dealing with quantities like kinetic energy, which involves squaring velocity terms.
- Group constants and variables: $(-1 {imes} 4) {imes} (x^1 {imes} x^9)$.
- Multiply constants: $-1 {imes} 4 = -4$.
- Multiply variables using exponent rules: $x^1 {imes} x^9 = x^{10}$.
- Combine to get the final answer: $\boxed{{-4x^{10}}}$.
### Explanation
1. Understanding the problem
We are asked to simplify the expression $-x {imes} 4x^9$. This involves multiplying a constant and variables with exponents. We will use the properties of exponents to simplify the expression.
2. Rewriting the expression
First, we rewrite the expression as $-1 {imes} x^1 {imes} 4 {imes} x^9$.
3. Rearranging terms
Next, we rearrange the terms to group the constants and the variables: $(-1 {imes} 4) {imes} (x^1 {imes} x^9)$.
4. Multiplying constants
Now, we multiply the constants: $-1 {imes} 4 = -4$.
5. Multiplying variables
We multiply the variables using the exponent rule $x^a {imes} x^b = x^{a+b}$: $x^1 {imes} x^9 = x^{1+9} = x^{10}$.
6. Combining the results
Finally, we combine the results to get the simplified expression: $-4x^{10}$.
### 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 square with side length $2x^3$, its area is $(2x^3)^2 = 4x^6$. Simplifying expressions helps in physics when dealing with quantities like kinetic energy, which involves squaring velocity terms.
