I'm studying for a test so I want to make sure I'm doing these problems right.
Numerator (-5a exponent -2)
Denominator b3
All to the -1 exponent
For a= -4. And b=2
My answer I get is 1/10 is the right ?
-16 with -1/2 exponent
Would the answer be -4?
2-3 square root of 14
Would the answer be -1 square root 14 ?
5/square root 20 -2 square root 45
I get 2 as my answer is this right ?
3/y+2 + 2/y = 5y-4/y2-4
Got my LCD as y(y-2)(y+2)
I know you distribute LCD but idk how to solve ! Help please!!
It would be nice if you used standard notation for stuff.
-5a^-2/b^3 = (-5)(1/16)/8 = -5/128
(-5a)^-2/b^3 = (20)^-2/8 = 1/3200
How did you arrive at 1/10?
-16^(-1/2) = -1/4
Negative exponents mean reciprocals
(2-3)√14 is indeed -√14
5/√20 - 2/√45 = 5/(2√5) - 2/(3√5)
= 1/√5 (5/2 - 2/3)
11/(6√5) or 11/30 √5
3/(y+2) + 2/y = (5y-4)/(y^2-4)
clear denominators and you get
3y(y-2) + 2(y^2-4) = (5y-4)y
3y^2 - 6y + 2y^2 - 8 = 5y^2 - 4y
-2y - 8 = 0
y = -4
To solve these problems, let's go through each one step by step:
1. (-5a^(-2))^(-1) / b^3
To simplify this expression, we need to apply two rules of exponents:
First, a negative exponent can be rewritten as a positive exponent by taking the reciprocal. So, (-5a^(-2))^(-1) becomes 1/(-5a^(-2)).
Second, when we divide exponents with the same base, we subtract the exponents. So, we have 1/[-5 * (a^(-2) * b^3)].
Now, substitute the given values for a and b: 1/[-5 * ((-4)^(-2) * 2^3)].
Calculate the powers: 1/[-5 * (1/((-4)^2 * 8))].
Simplify: 1/[-5 * (1/(16 * 8))] = 1/[-5 * (1/128)] = 1/[-5/128].
Taking the reciprocal of a fraction is the same as flipping it, so we have: -5/128.
2. (-16)^(-1/2)
To evaluate this expression, raise -16 to the power of -1/2.
Substitute the given value: (-16)^(-1/2).
Calculate the power: 1/sqrt(-16).
Since the square root of -16 is not a real number, this expression is undefined. There is no valid answer.
3. 2 - 3√14
To simplify this expression, subtract the product of 3 and the square root of 14 from 2.
Calculate the square root of 14: ≈ 3.7417.
Substitute the value: 2 - 3 * 3.7417.
Simplify: 2 - 11.2251 = -9.2251.
4. (5 / √20) - (2 * √45)
To simplify this expression, perform the operations inside the parentheses.
Calculate √20: ≈ 4.4721.
Calculate √45: ≈ 6.7082.
Substitute the values: (5 / 4.4721) - (2 * 6.7082).
Simplify: 5 / 4.4721 - 2 * 6.7082 = 5/4.4721 - 13.4164.
To evaluate the subtraction of fractions and decimals, we need a common denominator.
Multiply the numerator and denominator of 5/4.4721 by ≈ 2.2361 (which is the square root of 5): 10.4721/10 - 13.4164.
Simplify: 10.4721/10 - 13.4164 ≈ 1.0472 - 13.4164 = -12.3692.
5. 3/(y + 2) + 2/y = (5y - 4)/(y^2 - 4)
Given that the Lowest Common Denominator (LCD) is y(y - 2)(y + 2), let's multiply each term by this LCD to eliminate the denominators.
Multiply the first term by y(y - 2)(y + 2), the second term by y(y - 2)(y + 2), and the third term by y(y - 2)(y + 2).
The equation becomes: 3y(y - 2)(y + 2)/(y + 2) + 2y(y - 2)(y + 2)/y = (5y - 4)y(y - 2)(y + 2)/(y^2 - 4).
Cancel out common factors where possible: 3y(y - 2) + 2(y - 2)(y + 2) = (5y - 4)y.
Expand and simplify each side of the equation: 3y^2 - 6y + 2(y^2 - 4) = 5y^2 - 4y.
Combine like terms: 3y^2 - 6y + 2y^2 - 8 = 5y^2 - 4y.
Continue simplifying: 5y^2 - 6y - 8 = 5y^2 - 4y.
Move all terms to one side of the equation: 5y^2 - 5y^2 - 6y + 4y - 8 = 0.
Combine like terms: -2y - 8 = 0.
Isolate the variable: -2y = 8.
Divide by -2 to solve for y: y = -4.
Therefore, the solution to the equation is y = -4.