4.4 Fractional Exponents and Radicals. Construct Understanding.
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Transcript of 4.4 Fractional Exponents and Radicals. Construct Understanding.
4.4 Fractional Exponents and Radicals
Construct Understanding
Construct Understanding
REMEMBER Grade 9?
𝒂𝒎
BASE
REMEMBER Grade 9?
𝒂𝒎
EXPONENT
REMEMBER Grade 9?
• = We can further use it to
calculate fractional exponents with numerator
1…
WHAT IS A FRACTIONAL EXPONENT?
𝒂xy
A FRACTIONAL EXPONENT with a
numerator 1
𝒂1y
• ==
Without a calculator, Calculate
√𝟓 • √𝟓= √𝟐𝟓 =𝟓What do you
notice?
• ==
=
√𝟓 • √𝟓= √𝟐𝟓 =𝟓andequivalent expressions
• ==
=
√𝟓 • √𝟓= √𝟐𝟓 =𝟓Similarly,
==
Without a calculator, Calculate
What do you notice?
==
and equivalent expressions
=
• ==
=
√𝟓 • √𝟓= √𝟐𝟓 =𝟓andequivalent expressions
This suggests
= =
=
Powers with Rational Exponents
= =
= When n is a natural number and x is a
rational number,
Evaluate each power without using a calculator
= = 3
= = 0.7
= =
POWERPOINT PRACTICE PROBLEMEvaluate each power without using a
calculator
What if….
The numerator in the exponent IS NOT 1?
𝟖𝟐𝟑𝟖
𝟏𝟑
= ??
RECALL..
=
So, for example,
=
=
=
= = 4
=
=
But, this is also true…
= =
=
But, this is also true…
=
=
=
= 4
=
Powers with Rational Exponents
When m and n are natural numbers and x is a rational number,
= =
AND
= =
a. Write in radical form in 2 waysb. Write and in exponent form. = ()² and
==
= =
= =
POWERPOINT PRACTICE PROBLEMa) Write in radical form in 2 waysb) Write and in exponent form.
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
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.
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.
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
Section 4.4 HOMEWORK
OPAGES: 227 – 228 OPROBLEMS: 3 - 22
QUIZOSections 4.1 – 4.3
OFriday, July 25