Question

Which expression is equivalent to the equation above

Answer 1

The correct answer is third option

p⁷q/160

Explanation:

Points to remember

1). ( xᵃ)ᵇ = xᵇ

2). x⁻ᵃ = 1/xᵃ

It is given that, (4p⁻⁴q)⁻²/10pq⁻³

To find the equivalent of (4p⁻⁴q)⁻²

(4p⁻⁴q)⁻² = 4⁻²p⁸q⁻²

= p⁸/4²q²

= p⁸/16q²

To find the equivalent of 10pq⁻³

1/10pq⁻³ = q³/10p

To find the equivalent of (4p⁻⁴q)⁻²/10pq⁻³

(4p⁻⁴q)⁻²/10pq⁻³ =p⁸q³/16q²10p = p⁷q/160

Therefore the correct answer is option 3

Answer 2

Answer: third option

Explanation:

The negative exponent rules establishes:

`a^(-n)=(1)/(a^n)`

The power to power property establishes:

`(a^b)^c=a^(bc)`

The quotien of power property establishes that when you divide two powers with equal base you must subtract the exponents.

Applying the properties, you obtain:

`((4p^(-4)q)^(-2))/(10pq^(-3))}=(q^3)/(10(4p^(-4)q)^(2))=(q^3)/(10p(16p^(-8)q^(2)))=(p^8q^3)/(160pq^2)=(p^7q)/(160)`