Help in solving this math problem?

Question

what is the value of (x+1)^-2/3 if x=7

any help and explaining is really appreciated.

Answer 1

Okay. You have a few things that you have to consider.

Negative exponents: moves it to the denominator
Fractional exponents: the denominator tells you what the root is, the numerator tells you what the root is rasied to

So: (x+1)^-2/3 rewritten would be:

1/[cuberoot(x+1)^2]

when x is seven you have
1/[cuberoot(8)^2]
1/[2^2]
1/4

Answer 2

One of the laws of exponents says that for any number, a, not equal to zero, and m>n, then a^m/a^n = a^(m-n). If n>m, then a^m/a^n = 1/a^(m-n). This is the case your problem presents here. (x+1)^-2/3 is equivalent to saying 1/(x+1)^2/3. Now we have to figure out how to evaluate (x+1)^2/3. Remember that fractional exponents can be read as raising the base number, in this case (x+1) to a power, m, and then extracting the nth root of the resulting number. Then (x+1)^2/3 can be read as the cube root of (x+1)^2, and can be written symbolically like this ((x+1)^2)^1/3. The usual shorthand method though is to use the radical sign over the expression with the index (the root being extracted), in the crook just before the radical symbol itself.

Now all we have to do is substitute 7 for x and crank out the result.

7+1 = 8, and 8 squared is 64.

Now we take the cube root of 64, which is 4. Finally, we divide 1 by 4 to obtain 1/4 or one quarter, and we are done.

Answer 3

If x= 7, x+1=8
(x+1)^-2/3 = 1/(x+1)^2/3
= 1/(8^2)^1/3
=1/(64)^1/3
=1/4

Answer 4

1/4 = 0.25

The ^-2/3 is the power of the sum of x and 1 (=8)

-2/3 means invert the sum of x and 1, then square it and take the cube root of it. The square of 1/8 = 1/64, and the cube root of 1/64 = 1/4 [(1/4)*(1/4)*(1/4) = 1/64]

So the denominator is 4 and the final value is 1/4 (0.25).

Answer 5

Substitute x=7 and you get:
(7+1)^-2/3
= 8^-2/3
Now let's look at the exponent: -2/3 as (-1)(2)(1/3)
So this means: invert; then square; then take the cube root
Or we can do it in any order we want since multiplication is commutative, so I woulddo:
cube root; then square then invert.

So let's to that to 8 and see what we get:

8 ---cube root ----> gives 2
2 ---- square ----> gives 4
4 ---- invert -----> gives 0.25

the answer is 0.25

Answer 6

work on what is on the inside of the() first ok, 7+1=8 then using the calculator 8^(-2/3)=0.25.

Answer 7

x=7
x+1=8

the power -2/3 means that the number is squared then cube-rooted, and then reciprocated (1/ the number)

therefore,
8² = 64

cube-rooted, becomes 4

its reciprocal = 1/4 = 0.25

the answer is 0.25

Answer 8

(x+1)^-2/3
x=7
plug 7 in for x
(7+1)^(-2/3)
8^(-2/3)
1/8^(2/3)
1/cube rt(8^2)
1/cube rt(64)
1/4

ANSWER
4