4.4 fractional exponents and radicals. construct understanding
TRANSCRIPT
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4.4 Fractional Exponents and Radicals
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Construct Understanding
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Construct Understanding
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REMEMBER Grade 9?
𝒂𝒎
BASE
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REMEMBER Grade 9?
𝒂𝒎
EXPONENT
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REMEMBER Grade 9?
• = We can further use it to
calculate fractional exponents with numerator
1…
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WHAT IS A FRACTIONAL EXPONENT?
𝒂xy
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A FRACTIONAL EXPONENT with a
numerator 1
𝒂1y
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• ==
Without a calculator, Calculate
√𝟓 • √𝟓= √𝟐𝟓 =𝟓What do you
notice?
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• ==
=
√𝟓 • √𝟓= √𝟐𝟓 =𝟓andequivalent expressions
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• ==
=
√𝟓 • √𝟓= √𝟐𝟓 =𝟓Similarly,
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==
Without a calculator, Calculate
What do you notice?
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==
and equivalent expressions
=
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• ==
=
√𝟓 • √𝟓= √𝟐𝟓 =𝟓andequivalent expressions
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This suggests
= =
=
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Powers with Rational Exponents
= =
= When n is a natural number and x is a
rational number,
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Evaluate each power without using a calculator
= = 3
= = 0.7
= =
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POWERPOINT PRACTICE PROBLEMEvaluate each power without using a
calculator
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What if….
The numerator in the exponent IS NOT 1?
𝟖𝟐𝟑𝟖
𝟏𝟑
= ??
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RECALL..
=
So, for example,
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=
=
=
= = 4
=
=
But, this is also true…
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= =
=
But, this is also true…
=
=
=
= 4
=
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Powers with Rational Exponents
When m and n are natural numbers and x is a rational number,
= =
AND
= =
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a. Write in radical form in 2 waysb. Write and in exponent form. = ()² and
==
= =
= =
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POWERPOINT PRACTICE PROBLEMa) Write in radical form in 2 waysb) Write and in exponent form.
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Biologists use the formula b = 0.01 to estimate the brain mass , b kilograms, of a mammal with body mass m kilograms. Estimate the brain mass each
animala. A husky with a body mass of 27 kg
b. A polar bear with a body mass of 200g
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Biologists use the formula b = 0.01 to estimate the brain mass , b kilograms, of a mammal with body mass m kilograms. Estimate the brain mass each
animala. A husky with a body mass of 27 kg
b. A polar bear with a body mass of 200g• Substitute: m = 27
b = 0.01b = 0.01b = 0.01b = 0.09 kg
The brain mass of the husky is approximately
0.09 kg.
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Biologists use the formula b = 0.01 to estimate the brain mass , b kilograms, of a mammal with body mass m kilograms. Estimate the brain mass each
animala. A husky with a body mass of 27 kg
b. A polar bear with a body mass of 200g• Substitute: m = 200
b = 0.01USE a
CALCULATOR!
The brain mass of the polar bear is approximately 0.34
kg.
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POWERPOINT PRACTICE PROBLEMUse the formula b = 0.01 to estimate the brain
mass of each animal.A moose with a body mass of 512 kg
A cat with a body mass of 5 kg
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Section 4.4 HOMEWORK
OPAGES: 227 – 228 OPROBLEMS: 3 - 22
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QUIZOSections 4.1 – 4.3
OFriday, July 25