The simplified expression by rationalizing the denominator is (C)
.First we must simplify the expression:

Then we factor the rational parts and cancel it out:

Then we rationalize the expression:

<span>Finally, the simplified expression by rationalizing the denominator is (C)

.</span>
Answer:
Below in bold.
Step-by-step explanation:
c) 3 x (9^2)^3/4 x ((81^3)^5/6
= 3 x 81^3/4 x 81^15/6
= 3 x 81^(3/4 + 15/6)
= 3 x 81^13/4
= 3 x 3^13
= 3^14
= 4,782,969.
f) (5x^-1y^2)^-2 / (25 x^2 y - 1)^2
= 5^-2 x^2y^-4 / 625 x^4y^-2
= 5^-2 x^-2 y^-2 / 5^4
= 5^-6 x^-2y^-2
= 0.000064x^-2y^-2.
Answer:48
Step-by-step explanation:
Total number of students=397
Students that travelled in a car=29
Let the students that travelled in a bus be represented by y.
Since 8 buses were filled, it will be 8y for total students
8y + 29= 397
8y= 397-29
8y= 368
Divide both side by 8
8y/8=368/8
y = 46
Number of students in each bus is 46
We are asked to find the area of the rectangle that has side lengths of 3/4 yard and 5/6 yard.
We know that area of rectangle is width times length.
To find the area of the given rectangle we will multiply both side lengths as:






Therefore, the area of the given rectangle would be
square yards.