# Exponents and Exponential Functions

## Common Core Standards

### Core Standards

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• N.RN.A.2 — Rewrite expressions involving radicals and rational exponents using the properties of exponents.

• N.RN.B.3 — Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

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• 8.EE.A.1

• 8.EE.A.2

• 8.NS.A.1

## Criteria for Success

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1. Understand that ${x\sqrt[n]{a}+y\sqrt[n]{a}=(x+y)\sqrt[n]{a}}$.
2. Understand that radicals with different indices or radicands cannot be combined.
3. Apply the properties of exponents and properties of operations to add and subtract rational exponent and radical expressions.
4. Understand that a rational number added to or subtracted from a rational number is rational, and a rational number added to or subtracted from an irrational number is irrational.

## Anchor Problems

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### Problem 1

The statement below is incorrect. Explain why it is incorrect and then correct the statement.

${\sqrt9+\sqrt9=\sqrt{18}}$

Which statements below are true? Select all that apply.

a.   ${2\sqrt3+\sqrt3=3\sqrt3}$

b.   ${10\sqrt5-5\sqrt5=5}$

c.   ${\sqrt2+\sqrt[3]{2}=2\sqrt2}$

d.   ${4\sqrt8-3\sqrt8=\sqrt8}$

e.   ${5\sqrt{8}-2\sqrt{6}=3\sqrt2}$

f.   ${8\sqrt[n]{x}-6\sqrt[n]{x}=2\sqrt[n]{x}}$

### Problem 2

Compute and simplify.

a.   ${\sqrt{48}+2\sqrt{27}-3\sqrt{12}}$

b.   ${-5\sqrt{20}-\sqrt{72}+\sqrt{125}}$

c.   ${(\sqrt[3]{16}+\sqrt[3]{54})^3}$

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

a.   ${\sqrt{8a}-\sqrt{32a}}$
b.   ${8\sqrt{18}-4\sqrt{8}-\sqrt{24}}$
c.   ${\sqrt{3}(2\sqrt{18}+\sqrt{32})}$