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Polynomial division

PART ONE:

solve:

(3n^5 w)^2 /(n^3 w)^0

A) 0

B) 9n^7w

C) 6n^4w

D) 9n^10w^2

PART TWO:

solve:

9c^7 w^-4 (-d^2)/(15c^3 w^6 (-d)^2)

A) 3c^4d^2/5w^10

B) 3c^4/5w^2

C) 3c^4/5w^10

D) -3c^4/5w^10

PART THREE:

solve:

5m^-3 /6^-1 m^-2

A) -5m/6

B) 30/m

C) 30m

D) -5/6m

PART FOUR:

solve:

6+ the square root of 2 / 3- the square root of 2

A) 18+ the square root of 2 / 9- the square root of 2

B) 18 + the square root of 2 / 7

C) 20/7

D) 20 + 9 times the square root of 2 / 7

PART FIVE:

solve:

18 / 9^3/2

A) 18^3 times the square root of 81

B) 2 times the square root of 9 / 9

C) 2/3

D) 3/2

Solution Preview

PART ONE:
(3n^5 w)^2 /(n^3 w)^0 == ??
Note: I have used * to denote multiplication and make the notations clearer.
Anything raised to the power of 0 is ALWAYS equal to 1. Therefore the denominator which is ((n^3)*w)^0 = 1. And any entity divided by 1 remains unchanged. So we are left with only the numerator which is
(3*(n^5)*w)^2.
In order to evaluate a 'product' raised to a power, we must raise each of the 'members' of the 'product' to the same power. So in our case the 'product' is (3*(n^5)*w). So you raise each member to the same power, which is 2.
Thus, (3*(n^5)*w)^2 = ...

Solution Summary

This shows how to simplify fractions that involve polynomials and square roots.

$2.19