These questions are a bit odd. On top of the exact point that the arrow is pointing at --->√ is a 4. So the radical form looks like this: √16^3 except for the four that is explained above.
His book wants to know the Exponential Form and the Standard form.
Then for the the next question it gives (like above) the radical form and instead of a four there is a three.
So the radical form is (√-27) ^2 .
They wish to know what the Exponenetial form and the Standard form.
Thankyou for answering and trying to understand my words that are total rubbish to even myself.
2007-05-22 05:09:43 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The fourth root of 16 is 2
Two cubed is 8
cube root of -27 is -3
(-3) squared is 9
2007-05-22 05:16:01 · answer #1 · answered by fred 5 · 0⤊ 0⤋
Oh, I've got it now. You mean the radical has a 4 over the little v. That means the fourth root or to the 1/4 power. So, the exponential form is
[16^(1/4)]^3 or 16^(3/4). The standard form would then be 8, since the positive fourth root of 16 is 2 raised to the third power is 8.
The next one is [(-27)^(1/3)]^2 or (-27)^(2/3)
The cube root of -27 is -3 then squared is 9.
2007-05-22 12:24:06 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The "4" above the radical sign means that you are taking the fourth root. The fourth root of 16 is 2. So fourth root(16)^3 = 2^3 = 8. I think by "exponential form" they mean 16^{3/4}.
For the other problem the exponential form is (-27)^{2/3}. In words you can read it as "the third root of -27 squared." The third root of -27 is -3, and so this squared is 9.
2007-05-22 12:20:31 · answer #3 · answered by Sean H 5 · 0⤊ 0⤋
What you're talking about is called a fourth-root. It can be easily expressed in decimal form. Recall that something of the form â(2) can be expressed as 2^(1/2)....
So,
This is how i will express fourth-root: 4â16^3
4â16^3 = 16^(3/4) (exponential form)
This can also be expressed as:
4â( 4*4*4*4*4*4), since it is fourth-root, pull groups of four like terms from the radical....
4â( 4*4*4*4*2*2*2*2) = 4*2 = 8 (standard form)
Similarly, (3â-27) ^2 = (-27^(1/3))^2 = -27 ^ (2/3) (exp form)
and, (3â-27) ^2 = 9 (standard form)
2007-05-22 12:23:18 · answer #4 · answered by mark r 4 · 0⤊ 0⤋
The first is a fourth root. The fourth root of 16 is 2. 2^3 = 8.
The second one is a third root. The third root of -27 is -3. If you square it, you get 9.
2007-05-22 12:15:24 · answer #5 · answered by TychaBrahe 7 · 0⤊ 0⤋