Question

@phi @mathmale @welshfella Question in comments:)

Answer 1

...??

Answer 2

A rectangle has a length of \[\sqrt[5]{16} =\]Heighth and a width of \[2_{5}^{1}\] Find the area of the rectangle.

Answer 3

The first exponent is length not height :/

Answer 4

is that
\[2\frac{ 1 }{ 5 } or 2^{\frac{ 1 }{ 5}}\]

Answer 5

how can you write "5th root" using exponents?

Answer 6

\[2^{\frac{ 1 }{5 }}\]

Answer 7

OK - makes sense - so
how can you write "5th root" using exponents?

Answer 8

\[16^{5}?\]

Answer 9

it's
\[16^{\frac{ 1 }{ 5 }}\]

so write the expression for the area, using the lenght and width in exponent form

Answer 10

\[16^{\frac{ 1 }{5? }} + 2 ^{\frac{ 1 }{ 5 }} ?\]

Answer 11

That doesn't seem right..:/

Answer 12

well area = width TIMES length

you have written PLUS

so now look and see that
\[a^{x} \times b ^{x} = (ab)^{x}\]

So simplify your expression like that

Answer 13

Would it be \[2^{\frac{ 4 }{ 5 }}\]

Answer 14

Because the square root of 16 is 4. There was 5 as an exponent so... \[\frac{ 4 }{ 5 } \times \frac{ 1 }{ 5 } = 2 \frac{ 4 }{ 5 }\]

Answer 15

your answer should have been
\[16^{\frac{ 1 }{ 5 }}\times 2^{\frac{ 1 }{ 5 }}\]

So simplify that using the method I gave above

Answer 16

Oh ok:)

Answer 17

Wait I'm really confused now.

Answer 18

don't panic

slow down and go back and read what we said

then use my example to simplify your equation

Answer 19

Let's review:

We know that length = 5th root (16)
And the is the same as \[16^{\frac{ 1 }{ 5 }}\]

And we know tha the width is
\[2^{\frac{ 1 }{ 5}}\]

And we know area= lenght xwidth
or
\[A = 16^{\frac{ 1 }{ 5}} \times 2^{\frac{ 1 }{ 5 }}\]

OK?

Answer 20

I am so sorry! My computer died !

Answer 21

so do you see what we did above...?

Answer 22

Yes, so I would multiply them. Would I turn them improper then?

Answer 23

@MrNood

Answer 24

?

Answer 25

a=3440 ?

Answer 26

Well seeing that my answer choices only start with two I suggest your wrong, but thans for the other 3338. Maybe you could turn that into people helping me?

Answer 27

the trick in this one is knowing 16 is 2^4
so
do
\[ (2^4)^\frac{1}{5} \cdot 2^\frac{1}{5} \]

Answer 28

now you use rules about exponents
(2^4)^(1/5) can be written as 2^(4/5)
(by multiplying 4*1/5 to get a "new" exponent)

Answer 29

Do I need to turn them improper?

Answer 30

no. once you have the same base (2 in this case)
you add the exponents (when multiplying)

easy example: \( 2^1 \cdot 2^2 = 2^3 \)
in this problem: \(2^\frac{4}{5} \cdot 2^\frac{1}{5} = \)?

Answer 31

you can add the exponents, so add 4/5 plus 1/5
the fractions have the same denominator so you add the tops (numerators)
and keep the denominator as 5

Answer 32

lost ?

Answer 33

Would it be 2 square?

Answer 34

do you know how to add 4/5 + 1/5 ?

Answer 35

it would be cheating (a bit) but, you could use a calculator to add 4/5 + 1/5
what do you get ?

Answer 36

4/5 + 1/5 = 1 I know that. Its just all of my answer choices start with 2.

Answer 37

yes, so what we are doing is width times height:
\[ \sqrt[5]{16} \cdot 2^\frac{1}{5} \]
we changed the "root" to the equivalent "exponent" form:
\[ \sqrt[5]{16} = 16^\frac{1}{5} \]

\[ 16^\frac{1}{5} \cdot 2^\frac{1}{5} \]

we then changed 16 to \(2^4\) (2*2*2*2 is 16)
\[ (2^4)^\frac{1}{5} \cdot 2^\frac{1}{5} \]

we then use the rule to simplify the first part:
\[ 2^\frac{4}{5} \cdot 2^\frac{1}{5} \]

now we know if we multiply the same base (2 here) we add the exponents
\[ 2^\frac{4}{5} \cdot 2^\frac{1}{5} =2^1\]

Answer 38

And 2 ^1 is the answer. ?

Answer 39

yes, but because 2^1 is 2 we write it simply as 2

Answer 40

Ok thanks! I have a few more can u help[?