Power Up Practice Worksheet
Power Up Practice
EXPONENT & RADICAL CHALLENGE
Name: ______________________
Date: _______________________
SECTION 01
Exponent Essentials
Simplify each expression using the product, quotient, or power rules. Leave answers in exponent form.
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\(x^5 \cdot x^9\)
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\((4m^3)^2\)
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\(\frac{y^{12}}{y^4}\)
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\((a^2 \cdot b^3)^4\)
SECTION 02
The Power of None & Negative
Simplify and evaluate. Ensure all exponents are positive in your final answer.
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\(2^{-3}\)
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\((12x^2 y^0)\)
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\(\frac{x^{-4}}{x^2}\)
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\((\frac{2}{3})^{-2}\)
SECTION 03
Radical Transformations
Convert each expression from radical to rational exponent form, or vice-versa.
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\(\sqrt[3]{x^5}\)
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\(y^{\frac{4}{7}}\)
The Ultimate Power Up
Simplify completely: \(\left( \frac{16x^8y^2}{4x^2y^{-4}} \right)^{\frac{1}{2}}\)
Power Up Answer Key
Power Up Practice
ANSWER KEY
TEACHER USE ONLY
SECTION 01
Exponent Essentials
- \(x^5 \cdot x^9\)
\(x^{14}\)
- \((4m^3)^2\)
\(16m^6\)
- \(\frac{y^{12}}{y^4}\)
\(y^8\)
- \((a^2 \cdot b^3)^4\)
\(a^8 b^{12}\)
SECTION 02
The Power of None & Negative
- \(2^{-3}\)
\(\frac{1}{2^3} = \frac{1}{8}\)
- \((12x^2 y^0)\)
\(12x^2\)
- \(\frac{x^{-4}}{x^2}\)
\(\frac{1}{x^6}\)
- \((\frac{2}{3})^{-2}\)
\((\frac{3}{2})^2 = \frac{9}{4}\)
SECTION 03
Radical Transformations
- \(\sqrt[3]{x^5}\)
\(x^{\frac{5}{3}}\)
- \(y^{\frac{4}{7}}\)
\(\sqrt[7]{y^4}\)
The Ultimate Power Up
Simplify completely: \(\left( \frac{16x^8y^2}{4x^2y^{-4}} \right)^{\frac{1}{2}}\)
\( (4x^6y^6)^{\frac{1}{2}} \)
\( 2x^3y^3 \)
Power Play Anchor Chart BW
Power Play
Exponent & Radical Laws
Exponent Laws
Product Rule ADD POWERS
\(a^m \cdot a^n = a^{m+n}\)
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\(x^3 \cdot x^4 = x^7\)
Quotient Rule SUBTRACT POWERS
\(\frac{a^m}{a^n} = a^{m-n}\)
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\(\frac{y^8}{y^2} = y^6\)
Power of a Power MULTIPLY POWERS
\((a^m)^n = a^{m \cdot n}\)
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\((z^2)^5 = z^{10}\)
Zero Exponent ALWAYS ONE
\(a^0 = 1\)
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\(15^0 = 1\)
Radical & Rational
Negative Exp. RECIPROCAL
\(a^{-n} = \frac{1}{a^n}\)
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\(x^{-3} = \frac{1}{x^3}\)
Rational Exp. ROOT & POWER
\(a^{\frac{m}{n}} = \sqrt[n]{a^m}\)
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\(x^{\frac{2}{3}} = \sqrt[3]{x^2}\)
Radical Prod. COMBINE BASE
\(\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}\)
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\(\sqrt{12} = \sqrt{4} \sqrt{3}\)
Radical Quot. SPLIT FRACTION
\(\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}\)
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\(\sqrt{\frac{9}{4}} = \frac{3}{2}\)
Bases must match to use exponent rules!
