Skip to content

Radicals and Integer Exponents

Apply properties of integer exponents and work with square and cube roots.

Written and reviewed by the Study Mondo Education TeamLast updated
🎯⭐ INTERACTIVE LESSON

Try the Interactive Version!

Learn step-by-step with practice exercises built right in.

Start Interactive Lesson →

Radicals and Integer Exponents

Rules of Exponents

RuleFormulaExample
Productam⋅an=am+na^m \cdot a^n = a^{m+n}x3⋅x4=x7x^3 \cdot x^4 = x^7
Quotientaman=am−n\frac{a^m}{a^n} = a^{m-n}x5x2=x3\frac{x^5}{x^2} = x^3
Power of a power(am)n=amn(a^m)^n = a^{mn}(x3)2=x6(x^3)^2 = x^6
Zero exponenta0=1a^0 = 1 (a≠0a \neq 0)50=15^0 = 1
Negative exponenta−n=1ana^{-n} = \frac{1}{a^n}2−3=182^{-3} = \frac{1}{8}

Scientific Notation

A number in scientific notation: a×10na \times 10^n where 1≤a<101 \leq a < 10.

Examples:

  • 45,000=4.5×10445,000 = 4.5 \times 10^4
  • 0.003=3×10−30.003 = 3 \times 10^{-3}
  • 6,020,000=6.02×1066,020,000 = 6.02 \times 10^6

Operations with Scientific Notation

Multiply: (3×104)(2×105)=6×109(3 \times 10^4)(2 \times 10^5) = 6 \times 10^9

Divide: 8×1074×103=2×104\frac{8 \times 10^7}{4 \times 10^3} = 2 \times 10^4

Square Roots and Cube Roots

x=x1/2x3=x1/3\sqrt{x} = x^{1/2} \qquad \sqrt[3]{x} = x^{1/3}

36=6273=3−83=−2\sqrt{36} = 6 \qquad \sqrt[3]{27} = 3 \qquad \sqrt[3]{-8} = -2

Simplifying Square Roots

50=25⋅2=52\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}

72=36⋅2=62\sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2}

Tip: Find the largest perfect square factor when simplifying radicals.

Explain using:
Next Topic →
Solving Linear Equations
🎴

Practice with Flashcards

Rate this topic's cards with spaced repetition. Cards join your deck when you finish a topic's lesson and take its exit quiz.

📖

Browse All Topics

Explore more Grade 8 Math topics

📌 Related Topics in Expressions and Equations

Solving Linear Equations

❓ Frequently Asked Questions

What is Radicals and Integer Exponents?▾
Apply properties of integer exponents and work with square and cube roots.
How can I study Radicals and Integer Exponents effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Regular review and active practice are key to retention.
Is this Radicals and Integer Exponents study guide free?▾
Yes — all study notes, flashcards, and practice problems for Radicals and Integer Exponents on Study Mondo are free to access. No account is needed.
What course covers Radicals and Integer Exponents?▾
Radicals and Integer Exponents is part of the Grade 8 Math course on Study Mondo, specifically in the Expressions and Equations section. You can explore the full course for more related topics and practice resources.