Question

Which Expression Is Equivalent To The Expression Shown?

Answer 1

Lol. I hate Iready. but it think its the bottom left.
because with numbers that have negative exponents, you're suppose to put them over one to get it positive.
ex. 3^-4= 1/3^4
vice versa with the negative sign

Answer 2

The expression equivalent to
`3^7*3^(-4)` is
`3^7*(1)/(3^4)`

Explanation:

To answer this question, we notice that we have two factors multiplying each other. On one hand we have 3⁷, and on the other hand we have 3⁻⁴.

As the two factors are powers of the number 3, we have the following identities:

`3^7*3^(-4)=3^(7-4)=3^3=27`

and

`27\\eq3^(-28)=4.37*10^(-14)`

which discard that expression. We also know that if we multiply two factors with the same sign, we would get a positive number, so this discards the expression 3⁷x (-3⁴), as this resulting number will be negative (and 9 is positive).

Finally, we can write the following identity

`3^7*(1)/(3^(-4)) =3^7*(3^(-4))^(-1)=3^7*3^4=3^(7+4)=3^11=177147\\eq27`

Therefore the correct answer is
`3^7*(1)/(3^4)`