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