SAT Math formula sheet · all 24 · Advanced Math · #5 of 24

Exponent rules on the SAT: How It Is Tested

Equivalent expressions

Exponent Rules diagram for the SAT: Three rules, in order. Multiplying means add the exponents, dividing means subtract the exponents, and an exponent raise
What it is really testingThree rules, in order. Multiplying means add the exponents, dividing means subtract the exponents, and an exponent raised to another exponent means you multiply the exponents.

The question from the sheet

Medium
SAT Advanced Mathanswer A
Which expression is equivalent to h12q5h4q17\frac{h^{12}q^{5}}{h^{4}q^{17}}, where h>0h > 0 and q>0q > 0?
✓h8q12\frac{h^{8}}{q^{12}}
Bh8q12h^{8}q^{12}
Cq12h8\frac{q^{12}}{h^{8}}
Dh16q22h^{16}q^{22}

How the diagram applies

  1. Dividing like bases: subtract the exponents, one base at a time.
  2. h12−4=h8h^{12 - 4} = h^{8} and q5−17=q−12q^{5 - 17} = q^{-12}.
  3. A negative exponent moves the term to the bottom: h8q12\dfrac{h^{8}}{q^{12}}.

Answer: A

That is 1 of 24.

The whole sheet is one page per formula, each one solved on a real SAT question. Print it, stick it on the wall, scan any diagram to get back here.

Download the sheet (PDF)Watch this one solved →

The PDF needs no account. The video, the clean diagrams and practice on this skill need a free one, and never a card.

All 24 diagrams

Common Questions

It comes up as an SAT equivalent expressions question. Three rules, in order. Multiplying means add the exponents, dividing means subtract the exponents, and an exponent raised to another exponent means you multiply the exponents.

Dividing like bases: subtract the exponents, one base at a time. h^12 - 4 = h^8 and q^5 - 17 = q^-12. A negative exponent moves the term to the bottom: h^8q^12.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Exponent Rules is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.