I can't do the following problem. I am not sure what to do when you have an algerbraic power & have to multiple it by a real number?
((x^ny^(m+3))^2)/x^(n+2)y^3-m)) * ((x^2y)/(x^(n-5)*y^(5-3m))
remember that when multiplying powers with the same base, we keep the base and ADD the exponents, and when dividing powers we
SUBTRACT the exponents.
my second line to your solution would be
x2n+2-n-2-n+5 y2m+6+1-3+m-5+3m
= x5y2
I hope I interpreted your expression correctly, since there appears to be an extra ")" in the part before the "*"
make that
= x5y2+6m
I guess it was anticipated wishfull thinking that the m's would also cancel
To simplify the given expression:
((x^ny^(m+3))^2)/x^(n+2)y^3-m)) * ((x^2y)/(x^(n-5)*y^(5-3m))
We can start by applying the power rule for exponents. When you have an algebraic expression raised to a power, you multiply the exponents.
Step 1: Simplify the numerator
In the numerator, we have (x^ny^(m+3))^2. To simplify this expression, we raise both x and y to the power of 2, separately:
(x^ny^(m+3))^2 = x^(2n)y^(2m+6)
Now our expression becomes:
(x^(2n)y^(2m+6))/x^(n+2)y^3-m) * ((x^2y)/(x^(n-5)*y^(5-3m))
Step 2: Simplify the denominator
In the denominator, we have x^(n+2)y^3-m. Again, let's apply the power rule to simplify it:
x^(n+2)y^3-m = x^(n+2)/(y^m)
Our expression now becomes:
(x^(2n)y^(2m+6))/(x^(n+2)/(y^m)) * ((x^2y)/(x^(n-5)*y^(5-3m))
Step 3: Combine like terms and simplify further
To divide by a fraction, we multiply by its reciprocal. So let's multiply the expression by the reciprocal of the denominator:
(x^(2n)y^(2m+6))/(x^(n+2)/(y^m)) * ((x^2y)/(x^(n-5)*y^(5-3m)) * ((y^m)/(x^(n+2)))
Now we can cancel out common factors:
(x^(2n)y^(2m+6))/(x^(n+2))/(x^(n-5)*y^(5-3m))
Since we have the same base, we subtract the exponents in the denominator:
= x^(2n) / x^(n+2-(n-5)) * y^(2m+6-5+3m)
Simplify further:
= x^(2n) / x^(-3) * y^(2m+6+3m-5)
= x^(2n) * x^(3) * y^(2m + 3m + 1)
= x^(2n + 3) * y^(5m + 1)
So, the simplified expression is:
x^(2n + 3) * y^(5m + 1)