Unit 2 • Lessons 4–6 (Exponents) — Quiz 2
Scientific notation • Rational exponents (convert, simplify, laws)
Sci. Notation × ÷
Normalize Mantissas
Fractional Exponents
Radical ↔ Exponent
Negative/Zero Powers
Practice Set
Each question allows 2 attempts. Use the built-in whiteboard to show your work, then click Reveal Solution if needed. Assume positive bases when taking even roots.
1) Scientific Notation
Write \(0.000045\) in scientific notation.
Move the decimal \(5\) places right: \(4.5\times10^{-5}\).
2) Standard Form
Convert \(6.2\times10^{7}\) to standard form.
\(6.2\times10^{7}=62{,}000{,}000\) (move decimal \(7\) places right).
3) Multiply in Sci. Notation
\((3.0\times10^{4})(2.5\times10^{-3})\)
Multiply mantissas \(3.0\cdot2.5=7.5\); add exponents \(4+(-3)=1\).
Result \(7.5\times10^{1}\) \((=75)\).
4) Divide in Sci. Notation
\(\dfrac{8.4\times10^{-5}}{2.1\times10^{-2}}\)
Divide mantissas \(8.4/2.1=4\); subtract exponents \(-5-(-2)=-3\).
Result \(4\times10^{-3}\).
5) Exponent ↔ Radical
Write \(x^{5/3}\) in radical form.
\(x^{5/3}=\sqrt[3]{x^{5}}=(\sqrt[3]{x})^{5}\). (Either form is fine; the simplest is \(\sqrt[3]{x^{5}}\).)
6) Simplify with Fractional Exponents
\(\dfrac{16a^{3/2}b^{1/2}}{4a^{1/2}b^{3/2}}\)
Coefficient \(16/4=4\). Exponents: \(a^{3/2-1/2}=a^1\); \(b^{1/2-3/2}=b^{-1}\Rightarrow 4a/b.\)
7) Evaluate a Rational Exponent
Evaluate \(27^{2/3}\).
\(27^{2/3}=(\sqrt[3]{27})^{2}=3^{2}=9.\)
8) Negative Fractional Exponent
Simplify \((64x^{6})^{-1/2}\).
\((64x^{6})^{-1/2}=\dfrac{1}{(64x^{6})^{1/2}}=\dfrac{1}{8x^{3}}\) (assuming \(x>0\)).
Progress
Score: 0/8