80^1/4
-------- <===divide (to make it easier for u to see)
5^-1/4
(16^5/9 * 5^7/9)^-3
I keep getting wrong answers and we have a test on tuesday, i don't wanna fail. Everyone in class is having problems understanding this.
-------- <===divide (to make it easier for u to see)
5^-1/4
(16^5/9 * 5^7/9)^-3
I keep getting wrong answers and we have a test on tuesday, i don't wanna fail. Everyone in class is having problems understanding this.
-
When working with fractional exponents, it's creating an exponent inside a "root." A negative exponent means to remove the negative sign and put the whole thing under 1.
Remember that the "top" number goes on the inside and the "bottom" number becomes the "root" number. These are tough to notate properly here, so I'll try to explain clearly!
For example:
x^(1/2) is the square root of x^1
x^-2 = 1 / (x²)
80^(1/4) means the 4th root of 80^1. This should be a √ with a little 4 above the "v" [I'll write it as (4th)√ ]
5^-(1/4) means the 4th root of 5^1, however, because it's negative, the whole thing gets put under a 1, like:
= (4th)√80^1 / 1/(4th)√5^1
Anything to the power of 1 equals itself, so we can simplify:
= (4th)√80 / 1/(4th)√5
To divide a fraction, we can "flip it" and change the / to a *
= (4th)√80 * (4th)√5/1
= (4th)√80 * (4th)√5 -- since these are both 4th roots, we can multiply the two "inside" numbers together and put it under the radical
= (4th)√(80 * 5)
= (4th)√(400)
= 2√5
(16^5/9 * 5^7/9)^-3
= [(9th)√(16^5) * (9th)√(5^7)]^-3
= [(9th)√(16^5 * 5^7)]-^3
= [(9th)√(1048576 * 78125)]-^3
= [(9th)√81920000000]-^3
= 1 / [(9th)√81920000000]^3
Remember that the "top" number goes on the inside and the "bottom" number becomes the "root" number. These are tough to notate properly here, so I'll try to explain clearly!
For example:
x^(1/2) is the square root of x^1
x^-2 = 1 / (x²)
80^(1/4) means the 4th root of 80^1. This should be a √ with a little 4 above the "v" [I'll write it as (4th)√ ]
5^-(1/4) means the 4th root of 5^1, however, because it's negative, the whole thing gets put under a 1, like:
= (4th)√80^1 / 1/(4th)√5^1
Anything to the power of 1 equals itself, so we can simplify:
= (4th)√80 / 1/(4th)√5
To divide a fraction, we can "flip it" and change the / to a *
= (4th)√80 * (4th)√5/1
= (4th)√80 * (4th)√5 -- since these are both 4th roots, we can multiply the two "inside" numbers together and put it under the radical
= (4th)√(80 * 5)
= (4th)√(400)
= 2√5
(16^5/9 * 5^7/9)^-3
= [(9th)√(16^5) * (9th)√(5^7)]^-3
= [(9th)√(16^5 * 5^7)]-^3
= [(9th)√(1048576 * 78125)]-^3
= [(9th)√81920000000]-^3
= 1 / [(9th)√81920000000]^3