Question

Which expression is equivalent to the equation above

Answer 1

Answer: third option

Step-by-step explanation:

The negative exponent rules establishes:

$a^{-n}=\frac{1}{a^n}$

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:

$\frac{(4p^{-4}q)^{-2}}{10pq^{-3}}}=\frac{q^3}{10(4p^{-4}q)^{2}}=\frac{q^3}{10p(16p^{-8}q^{2})}=\frac{p^8q^3}{160pq^2}=\frac{p^7q}{160}$

 

Answer 2

Answer:

The correct answer is third option

p⁷q/160

Step-by-step 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