Question

 

 

Can someone please help me?

 

I'm having a lot of trouble with simplifying these :(

1) h^-5u^4m/h^2u^-7m^3

2) (5z^10)(8z^2)/32z^9

3) (9y^10/3y^3)^-2

 

Answer 1

1) The expression (h^-5 u⁴ m)/(h²u^-7m³)

{Apply Negative Exponent Property a^-n = 1/aⁿ where a ≠ 0}

= (u⁴ m u⁷)/(h⁵ h² m³)

{Apply Product of Powers Property a^maⁿ = a^m+n}

= (u⁴⁺⁷ m )/(h⁵⁺² m³)

= (u¹¹ m )/(h⁷m³)

(h^-5 u⁴ m)/(h²u^-7m³) = (u¹¹)/(h⁷m²).

Answer 2

2) The expression (5z¹⁰ 8z²)/(32z⁹)

{Apply Negative Exponent Property a^-n = 1/aⁿ where a ≠ 0}

= (5z¹⁰ 8z²z^-9)/(8 * 4)

= (5z¹⁰z²z^-9)/4

= 5/4 (z¹⁰z²z^-9)

{Apply Product of Powers Property a^maⁿ = a^m+n}

= 5/4 (z^{10 + 2 - 9})

= 5/4(z³)

(5z¹⁰ 8z²)/(32z⁹) = 5z³/4.

Answer 3

3) The expression (9y¹⁰/3y³)^-2

^{{Apply Negative Exponent Property a-n = 1/an where a ≠ 0}}

= (3y¹⁰y^-3)^-2

{Apply Product of Powers Property a^maⁿ = a^m+n}

= (3y^10-3)^-2

= (3y⁷)^-2

= 1/(3y⁷)²

(9y¹⁰/3y³)^-2 = 1/9y¹⁴.