Unit 2 • Lessons 1–3 (Exponents) — Quiz 1
Whole-number powers • Combining exponent laws • Integral (zero & negative) exponents
Product/Quotient Rules
Power of a Power
Power of a Product
Zero Exponent
Negative Exponents
Practice Set
Each question allows 2 attempts. Use the built-in whiteboard to show your work, then click Reveal Solution if needed.
1) Power of a Power
Evaluate \((3^2)^3\).
\((3^2)^3=3^{2\cdot 3}=3^6=729.\)
2) Product Rule
Simplify \(2^4\cdot 2^3\).
\(2^4\cdot 2^3=2^{4+3}=2^7=128.\)
3) Quotient Rule
Simplify \(\dfrac{a^7}{a^3}\) for \(a\ne 0\).
\(\dfrac{a^7}{a^3}=a^{7-3}=a^4.\)
4) Power of a Product
Simplify \((2x^3y)^2\).
\((2x^3y)^2=2^2x^{3\cdot2}y^{2}=4x^6y^2.\)
5) Zero Exponent
Simplify \((5x^{-1}y^3)^0\) assuming variables are non-zero.
Any nonzero base to the zero power equals \(1\). Thus \((5x^{-1}y^3)^0=1\).
6) Negative Exponents & Quotients
Simplify \(\dfrac{x^{-3}y^{2}}{x\,y^{-4}}\).
\(x^{-3}/x=x^{-4}\) and \(y^{2}/y^{-4}=y^{2-(-4)}=y^{6}\Rightarrow \dfrac{y^{6}}{x^{4}}.\)
7) Power of a Power (with negatives)
Simplify \((a^{-2}b^{3})^{2}\).
\((a^{-2}b^{3})^{2}=a^{-4}b^{6}=\dfrac{b^{6}}{a^{4}}.\)
8) Mixed Laws
Simplify \(\dfrac{(3x^{2}y^{-1})^{3}}{9x^{-1}y^{2}}\).
Numerator: \((3x^{2}y^{-1})^{3}=27x^{6}y^{-3}\).
Divide by \(9x^{-1}y^{2}\): coefficient \(27/9=3\); \(x^{6-(-1)}=x^{7}\); \(y^{-3-2}=y^{-5}\).
Result \(=3x^{7}y^{-5}=\dfrac{3x^{7}}{y^{5}}\).
Progress
Score: 0/8