Late questions that are just testing classic exponent rules

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from ACT F11

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As you can see, this is #54, so we are almost at the end of the section. So it's a late question, what is supposed to be a real hard question.

But we look at what's going on in this question, and we see some exponents, and so we know that it's just going to be testing our awareness of the classic exponent rules:

1. When to add, subtract, or multiply exponents
2. What negative exponents mean
3. What fraction exponents mean
4. What an exponent of 0 means
5. Get the bases the same

If it's an exponent question, it's going to be testing some combination of this super classic stuff.

Right away, we see that we have two exponential terms multiplied by each other, and they both have the same base (x), so we know we are going to add those exponents together, so that it's x to the power of y+k.

So we know y+k is involved, so F and G are lookin real good.

The other side of the equation just says 1. How does an exponential term end up equalling 1? When the exponent is 0.

So, we can rewrite 1 as x^0. Because anything to the power of 0 equals 1. (And we should make it the same base as what's on the left side because we know we should be getting bases the same in an exponent question.....see #5 on the above list).

So, we have x to the power of y+k on the left side. And x to the power of 0 on the right side. Since the bases are the same, we can ignore the bases (that's one reason we make the bases the same), and just say y+k=0.

Nice.