Question

Which expression is NOT equivalent to the expression shown?

Answer 1

Hey there!

Let's first simplify this expression using our rules of exponents.

We know that:

1)   $(a^b)^c = a^{bc}$

And:

2)  $a^b + a^c = a^{b+c}$

Finally:

3)  $x^{b} /x^c = x^{b-c}$

One more:

4)  $a^0 = 1$

Now, we can simplify the top. Using our rule number 1<em />, we know we can just multiply the exponents to get 7^12. On the bottom, using our rule number 2, we know we can add out exponents to also get 7^12.

Without even simplifying the powers, we know that everything over itself if one. Therefore, in our answer choices, we're looking for everything not equal to one.

For the 7^12/7^12, we know that's what we just got so it equals one. For the 1, well, one equals one. For the next one, referring to our last rule, 4, anything to the power of 0 equals one, therefore that's also equal to one.

Now for our final answer choice. If we take another look at rule number 3, we know we have to subtract the exponent at the bottom from the one at the top because the exponents have the same base. That gives us 7^-24, and that surely does not equal one.

Therefore, your answer is:

$7^{12}/ 7^{36}$

Hope this helps!