Exponents

dacostaas · #1 $Old$ September 6th, 2008, 10:49 PM

Received three problems that r giving me a headache.

The first is R raised to the power 0.75 =24. Does this mean that I should convert 0.75 to 3/4 then multiply 24 by 3 and find the answer raised to the power 4?

(2) R squared +R squared =R cube . How is this possible?

(3) R raised to the power 0.5 - 90=0 Does this mean that I convert 0.5 to 1/2 and then find a number whose square root is 90 and do my calculations from there?

Jhevon · #2 $Old$ September 6th, 2008, 10:54 PM

Quote:

Originally Posted by dacostaas $View Post$

Received three problems that r giving me a headache.
0.75
The first is R =24. Does this mean that I should convert 0.75 to 3/4 then multiplY0 24 by 3 and find the answer raised to the power 4?
2 2 3
(2) R +R =R . How is this possible?
0.5
(3) R - 90=0 Does this mean that I convert 0.5 to 1/2 and then find a number whose square root is 90 and do my calculations from there?

first, please clarify. you can just type "^" to mean power. for example, x^2 means $x^2$ . no need to go through fancy formatting exercises. the forum takes out the spaces anyway, so you just waste your effort

do you mean

$R^{0.75} = 24$

$R^2 + R^2 = R^3$

and

$R^{0.5} - 90 = 0$ ?

dacostaas · #3 $Old$ September 6th, 2008, 11:01 PM

Yep. That's it. Just as it is on the paper.

Jhevon · #4 $Old$ September 6th, 2008, 11:22 PM

Quote:

Originally Posted by dacostaas $View Post$

Yep. That's it. Just as it is on the paper.

ok. so the first thing you should know is that raising something to a power is not the same as multiplying the something to the power.

for the first, raise both sides to the 1/0.75th power. this is the same as the 4/3rd power.

see post #3 here to see what we do when we have a fractional power.

for the second:

note that we have $2R^2 = R^3$

subtracting $2R^2$ from both sides, we get:

$R^3 - 2R^2 = 0$ ....now factorize

$\Rightarrow R^2 (R - 2) = 0$

Now what?

for the third:

add 90 to both sides

$\Rightarrow R^{1/2} = 90$

now it is just like the first question. you want to raise both sides to a power that will make the power of R 1 when multiplied. here, of course, that is 2

now continue

Shyam · #5 $Old$ September 6th, 2008, 11:23 PM

Quote:

Originally Posted by dacostaas $View Post$

Received three problems that r giving me a headache.

The first is R raised to the power 0.75 =24. Does this mean that I should convert 0.75 to 3/4 then multiply 24 by 3 and find the answer raised to the power 4?

(2) R squared +R squared =R cube . How is this possible?

(3) R raised to the power 0.5 - 90=0 Does this mean that I convert 0.5 to 1/2 and then find a number whose square root is 90 and do my calculations from there?

(1)Please see and try to understand

we know the exponent law: $a^{m} = b\; \Rightarrow a = b^{\frac 1{m}}$

$R^{0.75} = 24$

$\Rightarrow R = (24)^{\frac{1}{0.75}}$

$R = (24)^{\frac{4}{3}}$

$R = (24^4)^{\frac 1{3}}$

$R = \sqrt[3]{24^{4}}$

$R = \sqrt[3]{24^{3} \times 24}$

$R = 24 \sqrt[3]{24}$

$R = 24 \sqrt[3]{8 \times 3}$

$R = 24 \sqrt[3]{2^3 \times3}$

$R = 48 \sqrt[3]{3}$

(2) Please see here,

$R^2 + R^2 = R^3$

$2R^2 = R^3$

$2R^2 - R^3 =0$

$R^2 (2- R) =0$

$\Rightarrow R =0\; or \; R=2$

(3) Please see,

$R^{0.5} - 90 = 0$

$R^{0.5} = 90$

$R = (90)^{\frac {1}{0.5}}$

$R = (90)^{2}$

$R = 8100$

dacostaas · #6 $Old$ September 7th, 2008, 07:18 AM

Please explain step 5. Why do you multiply by 24? What's the reasoning behind this?

Jhevon · #7 $Old$ September 7th, 2008, 07:15 PM

Quote:

Originally Posted by dacostaas $View Post$

Please explain step 5. Why do you multiply by 24? What's the reasoning behind this?

he didn't multiply by 24 anywhere. he factored out 24 from underneath the root. do you see that now?