How to interpret correctly the use of exponents and brackets

[Probability]

Lets say I have; 7p^4. and then say I have (7p^4), and (7p)^4. In the first example I thought p was worked out first using the exponent, then multiplying by 7 to give the answer. In the second example I would have said the same, but in the third example I would have thought work out 7p and then work out the result to the exponent to give the answer. Now if I had a value for p, such as -1.29 and the question was written 7p^4, if I wrote it like this; 7(-1.29^4) would this be wrong? Now suppose I wrote this out like 7(-1.29)^4, given the original question said 7p^4, which is the correct way to express it to get the right answer?

 

[HallsofIvy]

The difference is that \(\displaystyle ( )^4\), the fourth power applies to everything inside the parentheses.

 

[Probability]

So if I have; 7p^4 - 4p^3 +16p^2 - 5p - 37 = 7 x -1.29^4 - 4 x - 1.29^3 + 16 x - 1.29^2 - 5 x - 1.29 - 37 = - 67.973 then I do the same again but this time using parentheses. 7 x (-1.29^4) - 4 x (- 1.29^3) + 16 x (- 1.29^2) - 5 x - 1.29 - 37 = -67.973 then I do the same again but this time using parentheses like this; (7 x -1.29)^4 (- 4 x - 1.29)^3 + (16 x - 1.29)^2 - 5 x - 1.29 - 37 = 24.047 all this is based on the expression above, am I to assume that the correct way to do it is this last method with solution 24.047

 

[HallsofIvy]

So if I have; 7p^4 - 4p^3 +16p^2 - 5p - 37 =

Are you saying that p= -1.29?

7 x -1.29^4 - 4 x - 1.29^3 + 16 x - 1.29^2 - 5 x - 1.29 - 37 = - 67.973 then I do the same again but this time using parentheses. 7 x (-1.29^4) - 4 x (- 1.29^3) + 16 x (- 1.29^2) - 5 x - 1.29 - 37 = -67.973 then I do the same again but this time using parentheses like this; (7 x -1.29)^4 (- 4 x - 1.29)^3 + (16 x - 1.29)^2 - 5 x - 1.29 - 37 = 24.047 all this is based on the expression above, am I to assume that the correct way to do it is this last method with solution 24.047

Be careful. "-1.29^4" is NOT the same as (-1.29)^4. The first is -7.6686282021340161 and the second is +7.6686282021340161.

 

[Probability]

NO! If p = -1.29, then above equals 24.04695767 ; you must bracket the (-1.29):
7 * (-1.29)^4 - 4 * (-1.29)^3 + 16 * (-1.29)^2 - 5 * (- 1.29) - 37
START using * as multiplication sign


NO again...can't tell what you're doing...very MESSY!
The 1st term = (7 * (-1.29))^4 = 6648.91837281 : so TRY AGAIN...

OK lets try this approach; 7*(-1.29)^4 -4*(-1.29)^3+16*(-1.29)^2 -5*(-1.29) - 37 = 24.07!

 

[lookagain]

OK lets try this approach; 7*(-1.29)^4 -4*(-1.29)^3+16*(-1.29)^2 -5*(-1.29) - 37 = 24.07!

Despite Denis stating "START using * as multiplication sign," a(b) is (also) standard for meaning the

product of a and b.

So either would work, but use the same one consistently throughout the expression.

In your expression, "-4" and "-5" are not read as "subtract four" and "subtract five," respectively.

They are the constants, -4, and -5, respectively. Put spaces between the "-" and the "4" and the "5,"

respectively, for the intent of subtraction. The expression actually equals 24.047 when rounded to

three decimal places.

The exclamation point doesn't belong in that line.

Recommendation: Some more horizontal spacing will make your expression easier to read,

e.g. where the plus sign is. Look at these suggestions for amendments:



7*(-1.29)^4 - 4*(-1.29)^3 + 16*(-1.29)^2 - 5*(-1.29) - 37 ~ 24.047


7(-1.29)^4 - 4(-1.29)^3 + 16(-1.29)^2 - 5(-1.29) - 37 ~ 24.047


\(\displaystyle 7(-1.29)\)^\(\displaystyle 4 \ - \ 4(-1.29)\)^\(\displaystyle 3 \ + \ 16(-1.29)\)^\(\displaystyle 2 \ - \ 5(-1.29) \ - \ 37 \ \approx \ 24.047\)


\(\displaystyle 7(-1.29)^4 \ - \ 4(-1.29)^3 \ + \ 16(-1.29)^2 \ - \ 5(-1.29) \ - \ 37 \ \approx \ 24.047\)