Simplify 3x4 y52x3 y72 cubicroot squareroot a11 b7 c9 Factor

Simplify. 3x^-4 y^5/(2x^3 y^-7)^-2 cubicroot squareroot a^11 b^7 c^9 Factor. 8x^2 - 14x + 3 8x^2 + 4x^2 - 18x - 9 10ax^2 - 23ax - 5a a^3 + b^3

Solution

1) (3x^-4y⁵)/(2x³y^-7)^-2

a^-m=1/a^m

=(3x^-4y⁵)/(1/(2x³y^-7)²)

=(3x^-4y⁵)(2x³y^-7)²

(ab)^m=a^m*b^m and (a^m)ⁿ=a^mn

=(3x^-4y⁵)(2²x^3*2y^-7*2)

=(3x^-4y⁵)(4x⁶y^-14)

a^m*aⁿ=a^m+n

=(3*4)x^-4+6y^5-14

=12x²y^-9

=12x²/y⁹

therefore  (3x^-4y⁵)/(2x³y^-7)^-2=12x²/y⁹

2)³(a¹¹b⁷c⁹)

=(a¹¹b⁷c⁹)^1/3

=a^11/3b^7/3c^9/3

=a^11/3b^7/3c³

therefore ³(a¹¹b⁷c⁹)=a^11/3b^7/3c³

3) 8x²-14x +3

= 8x²-12x-2x +3

=4x(2x-3) -1(2x-3)

=(2x-3)(4x-1)

therefore  8x²-14x +3=(2x-3)(4x-1)