Warm Up One Slides Daily Warm-Up • Set 1
5 Problems • 2 per Slide Max
Part A • Exponent Rules & Radicals
Algebra 1 - 8.1-8.4 Review
Warm-Up 1: Copy each expression into your template. Simplify using only positive exponents.
Product Rule
\(x^a \cdot x^b = x^{a+b}\)
Quotient Rule
\(\frac{x^a}{x^b} = x^{a-b}\)
Negative Rule
\(x^{-n} = \frac{1}{x^n}\)
Rational Rule
\(x^{\frac{m}{n}} = \sqrt[n]{x^m}\)
WARM-UP 1
Products & Powers
Simplify • Positive Exponents Only
Problem 01 Zero Exponent Rule
\(-2x^4 \cdot 3x^0 y^4\)
Remember: \(x^0 = 1\). Multiply numerical coefficients first.
Problem 02 Power of a Product
\((2x^2 y^{-3})^4 \cdot (-2x^2 y^3)\)
Raise coefficient \(2^4\), multiply powers, then combine like bases.
Write your steps in Box 1 & Box 2 on your Warm-Up 1 template.
2 Minutes
WARM-UP 1
Quotients & Rational Powers
Simplify Completely
Problem 03 Fraction & Negative Powers
\[\frac{4a^{-3}b^2}{-3a^3b^{-4}}\]
Relocate negative exponents across fraction bars to make them positive.
Problem 04 Numerical Rational Exponent
\(216^{\frac{2}{3}}\)
Evaluate root first: \((\sqrt[3]{216})^2\). Then calculate the square!
Write your steps in Box 3 & Box 4 on your Warm-Up 1 template.
2 Minutes
WARM-UP 1
Radical Form Conversion
Final Problem
Problem 05 Write in Radical Form
\((6b)^{\frac{1}{3}}\)
The denominator 3 becomes the index of the radical root: \(\sqrt[3]{\phantom{x}}\).
Record your radical expression in Box 5 . Self-assessment on next slide!
1 Minute
CHECK WORK
Warm-Up 1 • Solutions & Answers
Self-Assessment
\(-2x^4 \cdot 3x^0 y^4\)
\(-6x^4 y^4\)
\((2x^2 y^{-3})^4 \cdot (-2x^2 y^3)\)
\(-\frac{32x^{10}}{y^9}\)
\(\frac{4a^{-3}b^2}{-3a^3b^{-4}}\)
\(-\frac{4b^6}{3a^6}\)
\(216^{\frac{2}{3}} = (\sqrt[3]{216})^2 = 6^2\)
\(36\)
\((6b)^{\frac{1}{3}} \rightarrow\) Radical Form
\(\sqrt[3]{6b}\)
Record your score out of 5 in the Warm-Up 1 header on your template!
Warm-Up 1 Complete
Algebra Review Work Template Warm-Up 1 • 5 Questions
Algebra 1 - 8.1-8.4 Review
Copy each expression from the Warm-Up 1 slides. Show your steps and record final answers below.
Name:
Date: Per:
Score: ______ / 5
Product: \(x^a \cdot x^b = x^{a+b}\)
Quotient: \(\frac{x^a}{x^b} = x^{a-b}\)
Negative: \(x^{-n} = \frac{1}{x^n}\)
Rational: \(x^{\frac{m}{n}} = \sqrt[n]{x^m}\)
Problem 01 Work Space
Answer:
Problem 02 Work Space
Answer:
Problem 03 Work Space
Answer:
Problem 04 Work Space
Answer:
Problem 05 Work Space
Answer:
Show all steps to receive full credit. Circle or box your final answers.
Algebra 1 • Warm-Up 1
Warm-Up 2 • 5 Questions
Algebra 1 - 8.1-8.4 Review
Copy each expression from the Warm-Up 2 slides. Show your steps and record final answers below.
Name:
Date: Per:
Score: ______ / 5
Product: \(x^a \cdot x^b = x^{a+b}\)
Quotient: \(\frac{x^a}{x^b} = x^{a-b}\)
Negative: \(x^{-n} = \frac{1}{x^n}\)
Rational: \(x^{\frac{m}{n}} = \sqrt[n]{x^m}\)
Problem 01 Work Space
Answer:
Problem 02 Work Space
Answer:
Problem 03 Work Space
Answer:
Problem 04 Work Space
Answer:
Problem 05 Work Space
Answer:
Show all steps to receive full credit. Circle or box your final answers.
Algebra 1 • Warm-Up 2
Warm Up Two Slides Daily Warm-Up • Set 2
5 Problems • 2 per Slide Max
Part B • Exponent Rules & Radicals
Algebra 1 - 8.1-8.4 Review
Warm-Up 2: Copy each expression into your template. Simplify using only positive exponents.
Product Rule
\(x^a \cdot x^b = x^{a+b}\)
Quotient Rule
\(\frac{x^a}{x^b} = x^{a-b}\)
Negative Rule
\(x^{-n} = \frac{1}{x^n}\)
Rational Rule
\(x^{\frac{m}{n}} = \sqrt[n]{x^m}\)
WARM-UP 2
Products & Negative Powers
Simplify • Positive Exponents Only
Problem 01 Multiple Base Products
\(x^4 y^4 \cdot x^3 \cdot 3x\)
Add exponents of identical bases: \(x^4 \cdot x^3 \cdot x^1 = x^{4+3+1}\).
Problem 02 Power of a Power
\((y^{-4})^3 \cdot (-x^4 y^{-1})\)
Multiply powers: \((y^{-4})^3 = y^{-12}\). Move negative powers to bottom!
Write your steps in Box 1 & Box 2 on your Warm-Up 2 template.
2 Minutes
WARM-UP 2
Quotients & Rational Powers
Simplify Completely
Problem 03 Quotient Cancellation
\[-\frac{m^{-3}n^{-1}}{m^{-3}n^{-4}}\]
Notice \(m^{-3}\) cancels completely! Subtract powers of \(n\): \(-1 - (-4)\).
Problem 04 Negative Fractional Power
\(16^{-\frac{3}{2}}\)
Flip to denominator: \(\frac{1}{16^{3/2}}\). Take square root first, then cube.
Write your steps in Box 3 & Box 4 on your Warm-Up 2 template.
2 Minutes
WARM-UP 2
Exponential Form Conversion
Final Problem
Problem 05 To Exponential Form
\((\sqrt[3]{7r})^4\)
Remember: Index is the bottom denominator, power is the top numerator: \((base)^{\frac{p}{i}}\).
Record your exponential expression in Box 5 . Self-assessment next!
1 Minute
CHECK WORK
Warm-Up 2 • Solutions & Answers
Self-Assessment
\(x^4 y^4 \cdot x^3 \cdot 3x\)
\(3x^8 y^4\)
\((y^{-4})^3 \cdot (-x^4 y^{-1})\)
\(-\frac{x^4}{y^{13}}\)
\(-\frac{m^{-3}n^{-1}}{m^{-3}n^{-4}}\)
\(-n^3\)
\(16^{-\frac{3}{2}} = \frac{1}{(\sqrt{16})^3} = \frac{1}{4^3}\)
