Question

(-2p⁻⁵q . 4p⁵q⁻³)²

Explain with steps

Answer 1

`(64)/(q^(4))`

or

`64q^(-4)`

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)=(1)/(a^b)`

`64q^(-4)=(64)/(q^(4))`