Answer:
Step-by-step explanation:
9.
Cancel the common factor of 4y
-3x/7x^4 . (21x^5y^2)
Cancel the common factor of 7x^4
-3x .(3xy^2)
Multiply 3 by -3
-9x . (xy^2)
Raise x to the power of 1
-9(x^1x).y^2
Raise x to the power of 1
-9(x^1x^1) . y^2
Use the power rule a^m a^n = a^m+n to combine exponents
-9x^1+1 .y^2
-9x^2y^2, Thus final answer is -9x^2y^2
10.
Cancel the common factor of 3
-x^5/x^13 . 2x^10y/5y^2
cancel the common factor of x^10
-x^5/x^3 . 2y/5y^2
Multiply -x^5/x^3 by 2y/5y^2
Multiply 2 by -1
-x^5(2y)/x^3(5y^2)
Cancel the common factor of x^5 and x^3
-2x^2y/5y^2
Cancel the common factor of y and y^2
-2x^2/5y
Thus final answer = -2x^2/5y
11.
Cancel the common factor of 4x
y^11/x^7y^6 . 6x^8y/2x^2
Cancel the common factor of x^7y
y^11/y^5 . 6x/2x^2
Multiply y^11/y^5 and 6x/2x^2
y^11 (6x)/y^5 (2x^2)
Cancel the common factor of y^11 and y^5
y^6 (6x)/2x^2
Cancel the common factor of 6 and 2
y^6 (3x)/x^2
Cancel the common factor of x and x^2
y^6 . (3)/x
Move 3 to the left of y^6
3y^6/x Thus final answer = 3y^6/x
12.
Cancel the common factor of y^6
y^4/2x^3 . 20x^14/x
Cancel the common factor of 2x^3
y^4 . 10x^11/x
combine y^4 and 10x^11/x
y^4 (10x^11)/x
cancel the common factor of x^11 and x
y^4 (10x^10)
Rewrite using the commutative property of multiplication
10y^4 x^10, Thus final answer = 10y^4 x^10
13.
Combine
5x^-2 (2y^3)/3x . x^10
Multiply x by x^10 by adding the exponents(negative exponent rule
5x^-2 (2y^3)/3x^11 x2
Multiply x^11 by x^2 by adding exponents
5(2y^3)/3x^13
Multiply 5 by 2
10y^3/3x^13 thus final answer = 10y^3/3x^13
14.
Move x^-1 to the numerator using the negative exponent rule
(5xyx/8y^2)^2 . 26y^3/5x^2y^5
Multiply x by x by adding the exponents
(5x^2y/8y^2)^2 . 26y^3/5x^2y^5
Cancel the common factor of y and y^2
(5x^2/8y)^2 . 26y^3/5x^2y^5
Use the power rule (ab)^n = a^n b^n to distribute the exponent
5^2(x^2)^2/8^2y^2 . 26y^3/5x^2y^5
Simplify the numerator
25x^4/8^2y^2 . 26y^3/5x^2y^5
Simplify terms
65x^2/32y^4 Thus final answer is 65x^2/32y^4
