Question

Simplify each expression. The simplified expression should have no exponents. (40 points)

Answer 1

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