how do you evaluated this?
(-)sign
↓
_ __________( -11/-17)^-10
line is divide (9/5)^1/10
-(11/17^-10/(9/5)^(1/10)
use the y^x key, the most powerful key on your calculator
(-11/-17)^-10
= 1/(11/17)^10 = 77.725... (I stored that in A on my calculator)
(9/5)^(1/10) = 1.0605..
so -(11/17^-10/(9/5)^(1/10)
= -77.725... /1.0605...
= -73.28837824
I use the memories on my calculator to store the full numbers, never round them half way through the problem
do we need to reciprocal -(11/17) to -(17/11) ?
To evaluate the expression you provided, let's break it down step by step:
Step 1: Simplify the expression inside the parentheses.
(-11 / -17) = 11 / 17
Step 2: Simplify the expression outside the parentheses.
(11 / 17)^-10 = 1 / (11 / 17)^10
Step 3: Simplify the expression after the division symbol.
(9 / 5)^(1 / 10) = the 1/10th root of (9 / 5)
Now, let's combine all the simplifications:
(11 / 17)^-10 ÷ (9 / 5)^(1 / 10)
To evaluate this expression, you need to calculate each part separately and then perform the division.
Calculating (11 / 17)^-10:
- Raise the numerator (11) to the power of -10 and the denominator (17) to the power of -10:
(11^-10) / (17^-10)
- Calculate each part separately and then divide:
(1 / 11^10) / (1 / 17^10)
- Divide the two fractions:
17^10 / 11^10
Calculating (9 / 5)^(1 / 10):
- Take the 1/10th root of the numerator (9) and the denominator (5):
(9^(1/10)) / (5^(1/10))
Now, you have the result of each part:
A = 17^10 / 11^10
B = (9^(1/10)) / (5^(1/10))
Lastly, divide A by B to get the final result:
A ÷ B = (17^10 / 11^10) ÷ [(9^(1/10)) / (5^(1/10))]