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Master Radical to Rational Exponent Conversions | Math Guide

Grade 11 Math: Master Advanced Concepts & Skills

11FA.A1.1

Characteristics of quadratic functions

Applications of quadratic functions

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11FA.A1.2

Quadratic function in general form: y = ax^2 + bx + c

Quadratic function in vertex form: y = a(x-p)^2 + q

Multiplying polynomial by polynomial

11FA.A1.3

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

11FA.A1.4

Solving quadratic equations by factoring

11FA.A1.5

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

11FA.A1.6

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

11FA.A1.7

Nature of roots of quadratic equations: The discriminant

11FA.A1.8

Solving quadratic equations by completing the square

Applications of quadratic equations

11FA.A2.1

Identifying functions

Function notation

11FA.A2.2

Function notation (advanced)

11FA.A2.3

Domain and range of a function

11FA.A2.4

Introduction to quadratic functions

11FA.A2.5

Transformations of quadratic functions

11FA.A2.6

Combining transformations of functions

11FA.A2.7

Converting from general to vertex form by completing the square

11FA.A2.8

Completing the square

Completing the Square

11FA.A2.9

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

11FA.B1.1

Exponents: Rational exponents

Convert between radicals and rational exponents

11FA.B1.2

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Combining the exponent rules

11FA.B1.3

Graphing exponential functions

11FA.B1.4

Graphing transformations of exponential functions

11FA.B1.5

Finding an exponential function given its graph

11FA.B2.1

Exponential growth and decay by a factor

11FA.B2.2

Evaluating logarithms using change-of-base formula

Solving exponential equations using exponent rules

11FA.B3.1

Exponential growth and decay by percentage

11FA.B3.2

Exponential decay: Half-life

11FA.B3.3

Finance: Compound interest

Finance: Compound Interest

11FA.C1.1

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

11FA.C1.2

Combination of SohCahToa questions

11FA.C1.3

Law of sines

Ambiguous case: SSA triangles

Law of cosines

11FA.C1.4

Applications of the sine law and cosine law

11FA.C1.5

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

11FA.C2.1

Sine graph: y = sin x

11FA.C2.2

Cosine graph: y = cos x

11FA.C2.3

Tangent graph: y = tan x

11FA.C2.4

Cotangent graph: y = cot x

11FA.C2.5

Secant graph: y = sec x

11FA.C2.6

Cosecant graph: y = csc x

11FA.C2.7

Graphing transformations of trigonometric functions

11FA.C3.1

Determining trigonometric functions given their graphs

11FA.C3.2

Ferris wheel trig problems

11FA.C3.3

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

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Grade 11 Functions and Applications, University/College Preparation (MCF3M)

A. Quadratic Functions

B. Exponential Functions

C. Trigonometric Functions

math

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Ex. 1:

Ex. 2:

Ex. 3:

Intro

Converting a negative rational exponent to radical form

Handling a negative rational exponent by flipping and converting to radical form

Simplifying a negative rational exponent with a negative base

Simplifying a division of rational exponents and converting to radical form

<p>- Here we go. Okay, so we're now we're doing the opposite way here, right? We're trying to change into the exponent, and see if we can actually calculate it. It doesn't look like we can calculate it, because we've got a variable, right?<br />
We can change into an exponential forms. So this is my base number the "a. " Now, the idea is this: there's a power right here, right? That three will be a fraction on the top right there and divided by that root number five. So, your answer is just a to the power of three over five. Thanks for watching.</p>


Converting a radical with a variable base to rational exponent form

Rewriting 1 over the fourth root of 8^7 in exponential form

Evaluating a nested radical by converting to rational exponents

Multiplying cube roots by converting to rational exponents

Rewriting a fourth root with a negative exponent as a rational exponent

Simplifying a negative fifth root with a cubed radicand

Why fractional exponents equal radicals using exponent laws

We will learn how to convert between radicals and rational exponents in this lesson. Therefore, it is a good idea to brush up on your understanding of all the basic rules of exponents before stating to watch the lesson.