4.4 SAT Math - Negative Exponents

Negative Exponents are "flipped" – if a negative exponent appears in a denominator, move it to the numerator to make it positive and vice versa.

p+4 =

1 _________ p4

1 _________ p6

= p+6

y⁶•y^-2 = y⁴

 So a multiplication problem like this can be solved just like you would with positive exponents, by simply adding the exponents.  Since one of the exponents is negative, however, you end up with 6 + ^-2, which equals 4.

Starting SAT Score 650 and Above:

-Sat Math Hint: When you have a complicated-looking fraction, you can quickly "clean it up" by dividing your coefficients and subtracting your exponents:

 

Then, subtract your exponents.   Starting with p we have 9 - ^-2 = 11, then for s, -4 - 1 = -5 , and for t, since there's no t up top, we simply have 0 - 1 = -1.  So we are left with



We can now write this in three different ways.  We can leave it as above, or, we can eliminate the denominator entirely by writing the number as a fraction:

1/3p¹¹s^-5t^-1  

We could also write it only using positive exponents by "flipping" all the negative exponents into the other spot:

If the question asks for everything as positive exponents, you can also just start by "flipping" the negatives to make everything positive from the get-go:

3p9s-4 _________ 27p-2st

=

3p9p2 _________ 27s4st

And then cleaning up from there.

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