Question

Simplify each expression using the laws of exponents​

Answer 1

3.
`\sf x^4 *x^7=\bf x^(11)`

4.
`\sf x^5 *x^(-8)=\bf \cfrac{1}{x^3}`

5.
`\sf \cfrac{x^(-8)}{x^3}=\bf \cfrac{1}{x^(11)}`

Explanation:

3.
`\sf x^4 *x^7`

Apply the exponent rule:-

`\sf x^(4+7)`

Add numbers:-

`\sf x^(11)`

______________

4.
`\sf x^5 *x^(-8)`

Apply the exponent rule:-

`\sf x^(5-8)`

Subtract numbers:-

`\sf x^(-3)`

Apply the exponent rule:-

`\boxed{\sf \:a^(-b)=(1)/(a^b)}`

`\sf \cfrac{1}{x^3}`

_______________

5.
`\sf \cfrac{x^(-8)}{x^3}`

Apply the exponent rule:-

`\sf x^(-8-3)`

Subtract numbers:-

`\sf x^(-11)`

Apply the exponent rule:-

`\sf \cfrac{1}{x^(11)}`

______________________

Hope this helps!

Have a great day!