Question

Need help I'm stuck on my hw (this is multiple choice)

Answer 1

Let's solve step by step each problem:

A)

Here is important to use the multiplication property. When the base is the same you can sum the exponents:

`8^7*8^(-12)=8^(7+(-12))=8^(7-12)=8^(-5)`

Now you can see the exponent is negative and you can use another property to turn him positive. This can be done by inverting the fraction:

`8^(-5)=(1)/(8^5)`

8^5 is such a huge number and definitely, this answer will be between 0 and 1. Just showing you the value:

`(1)/(8^5)=0.00003`

B)

Here you have to use the division property. When the base is the same you can subtract the exponents:

`(7^4)/(7^(-3))=7^(4-(-3))=7^7=823543`

(not between 0 and 1)

C) Use the multiplication property that we used on letter A)

`((1)/(3))^2*((1)/(3))^9=((1)/(3))^(2+9)=((1)/(3))^(11)`
`((1)/(3))^(11)=(1^(11))/(3^(11))=0.000005^{}`

Between 0 and 1!

D) Use the division property that we used on letter B)

`((-5)^6)/((-5)^(10))=(-5)^((6-10))=(-5)^(-4)`
`(-5)^(-4)=(1)/((-5)^4)=0.0016`

Between 0 and 1! Therefore:

A, C and D are between 0 and 1.

B is not between 0 and 1.