I have two problems that I have done but I am not sure they are correct.
1) t^-5(t^2-t^4+5t) I got... 5t/t^7
2) -20(m^2v)(-v)^3 / 5(-v)^2(-m^4) I got.... 20(4v^2)/ 5m^2
You have to be much more specific regarding the order of operation here, use brackets please
e.g. you have 3 terms inside the bracket in the first question, but your answer is a single term, not very likely.
how do you do x2y(x+2)
To check if your solutions are correct, let's simplify each expression step by step:
1) t^-5(t^2 - t^4 + 5t)
To simplify this expression, we can first simplify each term inside the parentheses:
t^2 = t * t
t^4 = t * t * t * t
Substituting these values back into the expression:
t^-5(t * t - t * t * t * t + 5t)
Next, let's simplify the exponent t^-5:
t^-5 = 1 / (t^5)
Now we can rewrite the expression:
(1 / (t^5))(t * t - t * t * t * t + 5t)
Expanding the parentheses:
(t * t / (t^5) - t * t * t * t / (t^5) + 5t / (t^5))
We can simplify each term with the same base:
t * t / (t^5) = t^(2-5) = t^-3 = 1 / (t^3)
t * t * t * t / (t^5) = t^(4-5) = t^-1 = 1 / t
5t / (t^5) = 5t^(1-5) = 5t^-4 = 5 / (t^4)
Substituting these values back into the expression:
(1 / (t^3) - 1 / t + 5 / (t^4))
Now, we can combine the terms. To add or subtract fractions, we need to find a common denominator. In this case, the common denominator is (t^4):
((t^4 / (t^3 * t^4)) - (t^4 / (t * t^3 * t^4)) + (5 / (t^4)))
Simplifying the fractions:
((t^4 / (t^7)) - (t^4 / (t^8)) + (5 / (t^4)))
Combining the fractions:
(t^4 - t^4 + 5) / (t^7)
This simplifies to:
5 / (t^7)
So, your solution for the first problem is correct: 5 / (t^7)
Now let's move on to the second problem:
2) -20(m^2v)(-v)^3 / 5(-v)^2(-m^4)
To simplify this expression, we can start by simplifying the exponents:
(-v)^3 = (-1)^3 * v^3 = -v^3
(-v)^2 = (-1)^2 * v^2 = v^2
(-m^4) = (-1)^4 * m^4 = m^4
Substituting these values back into the expression:
-20(m^2v)(-v^3) / 5(v^2)(m^4)
Next, we can cancel out any common factors:
-20(m^2v)(-v^3) / 5(v^2)(m^4) = (-4 * 5)(m^2v)(-v^3) / (5v^2)(m^4)
Simplifying the coefficients:
-20 / 5 = -4
Canceling out common factors:
(-4)(m^2v)(-v^3) / (v^2)(m^4)
Simplifying the exponents further:
(-4)(m^2v)(-v^3) / (v^2)(m^4) = (-4)(m^2v)(-v^3) / (v^2)(m^4)
Finally, let's combine like terms:
(-4)(-v^3)(v^2)(m^2)(m^4)
Expanding the exponents:
= (-4)(-v^3)(v^2)(m^2)(m^4) = 4v^(2-3)m^(2+4)
= 4v^(-1)m^6 = 4(m^6 / v)
So, your solution for the second problem is incorrect. The correct simplification is 4(m^6 / v).