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

Answer:

The expression equivalent to $3^7*3^{-4}$ is $3^7*\frac{1}{3^4}$

Step-by-step 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

$27\neq3^{-28}=4.37\times10^{-14}$

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

$3^7*\frac{1}{3^{-4}} =3^7*(3^{-4})^{-1}=3^7*3^4=3^{7+4}=3^11=177147\neq27$

Therefore the correct answer is $3^7*\frac{1}{3^4}$