Question

(-2p⁻⁵q . 4p⁵q⁻³)²

Explain with steps

Answer 1

Answer:

$\frac{64}{q^{4}}$

or

$64q^{-4}$

Step-by-step explanation:

Remember the properties

Product rules

$a^{n} a^{m}=a^{n+m}$

Power rules

$(a^{n})^{m}=a^{n*m}$

we have

$(-2p^{-5}q4p^{5}q^{-3})^{2}$

Applying the product rules

$(-2(4)p^{-5+5}q^{-3+1})^{2}$

$(-8p^{0}q^{-2})^{2}$

$(-8q^{-2})^{2}$

Applying the power rules

$64q^{-4}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

$64q^{-4}=\frac{64}{q^{4}}$