I start the questioning in the Warm Up about what is a rational number, and therefore a rational exponent.

Calculus finds patterns between equations: For each possible radius 0 to rwe just place the unrolled ring at that location. Students should be familiar with the Laws of Exponents to apply to these problems. Realize that a filled-in disc is like a set of Russian dolls. Like evolution, calculus expands your understanding of how Nature works.

I take questions, and rework any problem that the student needs to see. Formulas are a means to an end, a way to express a mathematical truth. Look for and express regularity in repeated reasoning. But does it work in theory? Big things are made from little things.

A note on examples Many calculus examples are based on physics. Here are two ways to draw a disc: But calculus is hard! And sometimes the little things are easier to work with.

But most of us learn these formulas independently. Heat, motion, populations, …. Most of the students have not been introduced to rational exponents, and I want them to build a strong vocabulary and understanding of how the exponential expression and rational exponents are structured.

Image from Wikipedia This was a quick example, but did you catch the key idea? I show problem 8 and problem 9 in the video below. Using calculus, we can ask all sorts of questions: The Power Property - multiply exponents times exponents of powers to other powers.

The natural log can be seen as an integral, or the time needed to grow. Calculus relates topics in an elegant, brain-bending manner.

Arithmetic is about manipulating numbers addition, multiplication, etc. I think anyone can appreciate the core ideas of calculus. Calculus is similarly enlightening. But if we take thinner rings, that triangle becomes less jagged more on this in future articles.

Algebra finds patterns between numbers: You understand why drugs lead to resistant germs survival of the fittest. Calculus showed us that a disc and ring are intimately related:Simplify exponent expressions Question: Use the Law of Exponents to rewrite and simplify the expression.

(1) (a) (b) (2) (a) (b) (3) (a) (b) (4) (a) (b) Solution: Make sure to reference radical and exponent rules/laws to make sure you know all of the rules properly.

Use the Law of Exponents to rewrite and simplify the expression.

by The. Question: Use the Laws of Exponents to rewrite and simplify the expression. 4^-3/2^-8 1/3 squareroot x^4 4^-3/2^-8 1/3 squareroot x^4 Show transcribed image text Use the Laws of Exponents to rewrite and simplify the expression.

Simplify the following expression: This question is a bit different, because the larger exponent is on the term in the denominator. But the basic reasoning is the same. I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education.

Calculus relates topics in an elegant, brain-bending manner. Sec Simplify Expressions Using the Laws of Exponents Learning Objectives: 1. Use the laws of exponents to simplify expressions involving rational exponents.

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Use the laws of exponents to simplify radical expressions. then assuming the expression.

Sep 01, · Please help with calculus laws of exponents? use the laws of exponents to rewrite the expressions: A)4^-3 / 2^-8 B) 1/ the cube root of (x^2) Follow. 3 answers 3. Report Abuse.

Use the law of exponents to simplify the expression? 3 questions? Help please!?Status: Resolved.

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