Using the Laws of Exponents
Using the Laws of Exponents is a skill on Pengi from Lesson 1: Laws of Exponents in Yoshiwara Elementary Algebra.
Key Concepts
Property To simplify complex expressions, combine the laws of exponents while following the order of operations. Always simplify powers before performing multiplication. 1. $a^m \cdot a^n = a^{m+n}$ 2. $\frac{a^m}{a^n} = a^{m n}$ or $\frac{1}{a^{n m}}$ 3. $(a^m)^n = a^{mn}$ 4. $(ab)^n = a^nb^n$ 5. $(\frac{a}{b})^n = \frac{a^n}{b^n}$.
Examples Simplify $3a^2b(2ab^2)^3$. First, cube the term in parentheses: $3a^2b(8a^3b^6)$. Then multiply: $24a^{2+3}b^{1+6} = 24a^5b^7$. Simplify $( y)^2( yz)^3$. Simplify each power first: $y^2( y^3z^3)$. Then multiply: $ y^{2+3}z^3 = y^5z^3$. Simplify $(\frac{x^4}{2})^2(3x)^2$. Simplify powers: $(\frac{x^8}{4})(9x^2)$. Then multiply: $\frac{9x^{8+2}}{4} = \frac{9x^{10}}{4}$.
Explanation When expressions have multiple operations, always follow the order of operations (PEMDAS). Simplify any powers first, such as $(3x^2)^3$, before you multiply that result by other terms in the expression.
Common Questions
What is Using the Laws of Exponents?
Using the Laws of Exponents is a skill on Pengi from Lesson 1: Laws of Exponents in Yoshiwara Elementary Algebra.
What grade level is Using the Laws of Exponents for?
Using the Laws of Exponents is part of the Grade 6 Math curriculum, covered in Yoshiwara Elementary Algebra. It is designed for students studying Math at the Grade 6 level.
How can I learn Using the Laws of Exponents?
Pengi offers an AI-guided lesson for Using the Laws of Exponents that walks you through the key concepts step by step. The lesson is aligned to Yoshiwara Elementary Algebra so the content matches what you see in class.
How do I practice Using the Laws of Exponents?
After learning the concept, use the Practice mode to work through targeted exercises on Using the Laws of Exponents. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Using the Laws of Exponents?
Using the Laws of Exponents is covered in Yoshiwara Elementary Algebra, specifically in Chapter 9: More About Exponents and Roots under Lesson 1: Laws of Exponents. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Using the Laws of Exponents free to study on Pengi?
Yes, the core Learn and Practice modes for Using the Laws of Exponents are available for free on Pengi. No credit card is required to start studying.