Rational Exponents
Rational Exponents is a skill on Pengi from Lesson 3: Rational Exponents in Yoshiwara Intermediate Algebra.
Key Concepts
Property For a positive base $a$ and a rational exponent $\frac{m}{n}$ where $n \neq 0$: $$a^{m/n} = (a^{1/n})^m = (a^m)^{1/n}$$ To compute $a^{m/n}$, you can either take the $n$th root of $a$ first and then raise it to the $m$th power, or raise $a$ to the $m$th power and then take the $n$th root. The denominator of the exponent is the root, and the numerator is the power.
Examples To evaluate $64^{2/3}$, we can take the cube root of 64 first, which is 4, and then square it: $(64^{1/3})^2 = 4^2 = 16$.
For $ 8^{4/3}$, the exponent applies only to the 8. We find $(8^{1/3})^4 = 2^4 = 16$, so the expression equals $ 16$.
Common Questions
What is Rational Exponents?
Rational Exponents is a skill on Pengi from Lesson 3: Rational Exponents in Yoshiwara Intermediate Algebra.
What grade level is Rational Exponents for?
Rational Exponents is part of the Grade 7 Math curriculum, covered in Yoshiwara Intermediate Algebra. It is designed for students studying Math at the Grade 7 level.
How can I learn Rational Exponents?
Pengi offers an AI-guided lesson for Rational Exponents that walks you through the key concepts step by step. The lesson is aligned to Yoshiwara Intermediate Algebra so the content matches what you see in class.
How do I practice Rational Exponents?
After learning the concept, use the Practice mode to work through targeted exercises on Rational Exponents. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Rational Exponents?
Rational Exponents is covered in Yoshiwara Intermediate Algebra, specifically in Chapter 6: Powers and Roots under Lesson 3: Rational Exponents. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Rational Exponents free to study on Pengi?
Yes, the core Learn and Practice modes for Rational Exponents are available for free on Pengi. No credit card is required to start studying.