Precalculus Question... 16 to the -3/4?

16^(-3/4)
= ⁴√[16^(-3)]
= ⁴√[(2^4)^(-3)]
= ⁴√[(2^-3)^4]
= 2^(-3)
= 1/(2^3)
= 1/8 (0.125)

16^(-3/4) = (2^4)^(-3/4) = 2^[4*(-3/4)] = 2^(-3) = 1/(2^3) = 1/8

16^(-3/4)

bring it down 1/(16^3/4)

16= 2^4 soooo

1/((2^4)^3/4)

multiply the powers 4 *3/4 = 3
2 will be to the third power when all is said and done...

1/(2^3)
1/8

the two people who stated that's a circle with middle (3, 14) and radius 13 are maximum suitable. and you relatively ought to state the question, by way of fact if what they're requesting is the spinoff then there is greater to this. If that's what they pick then you definitely ought to tell apart implicitly to discover dy/dx. i'm uncertain if that's what you're searching for, and that i don't be responsive to if that's previous what you're gaining knowledge of yet it relatively is what you ought to do: x^2 + y^2 - 6x + 8y -one hundred forty four = 0 convey all y words to a minimum of one ingredient like so y^2 + 8y = -x^2 - 6x + one hundred forty four and differentiate keeping in suggestions once you differentiate the left ingredient you ought to even have dy/dx, so (2y + 8)dy/dx = -2x - 6 the main suitable ingredient is differentiated frequently now divide via 2y + 8 to get dy/dx via itself so finally dy/dx = y' = (-2x - 6)/(2y + 8)

=[(16^1/4)]^-3=2^-3=1/2^3=1/8

If you have a calculator just type in 16 ^ (-3/4). I'm guessing you want more explanation than that though. When you have a negative exponent, you simply need to solve the problem without the negative and switch the numerator and denominators.

So, for your problem:
1. Ignore the negative sign and solve the problem 16^(3/4) or 16^(.75)
2. 16^(3/4)=8, so if you have a -3/4, you will have to simply change the answer (8, which is really 8/1)* to 1/8.
*Remember, any whole number is really that number over 1

If you use a simpler example, like 2^(-1), think of the problem as 2^1. As you probably know, any number to the 1st is that number, so 2. But since the 1 is negative, the 2 will be switched to the denominator, so your answer is 1/2.
Good luck on your test!

EASY one

just remember your rules for exponents..
a minus sign means reciprical

16^(-3/4) = 1/16^(3/4)

the fraction exponent can be taken as TWO DIFFERENT ONES
THE top or numerator of the exponent is just a regular exponent
so 1/16^3^(1/4) = 1/(16*16*16)^(1/4) = 1/4096^(1/4)

the exponent 1/4 MEANS 4th root
an exponent 1/2 means square root
an exponent 1/3 means cube root
an exponent 1/n means nth root.

so 1/4096^(1/4) = 1/8

I hope that helps you a little understanding how to find the exponent value

you can check the work by doing the opposite
8 ^ 4 = 4096
and the cube root of 4096 = 16


so 1/16^(3/4) = 1/8

good luck

16^(-3/4) = 2^4^(-3/4) = 2^(-3/4 * 4) = 2^(-3) = 1/2^3 = 1/8

16^-3/4
since 4th root of 16 is 2 then you can write it like this
2^-3 = 1/2^3
which is equal to 1/8

hope this helps!

Meg P is right, and the 4 root is 1/8

good luck