Question

ALGEBRA TWO HELP!!!!!!!!!!!!

Answer 1

Answer: p⁻¹ q⁴ r⁸

Explanation:

Use the quotient rule:
`(x^a)/(x^b)=x^(a-b)`

`(p^(-4)q^5r^6)/(p^(-3)qr^(-2))=p^(-4-(-3))q^(5-(1))r^(6-(-2))\\\\.\qquad \qquad =p^(-4+3)q^(5-1)r^(6+2)\\\\.\qquad \qquad =p^(-1)q^(4)r^(8)`

Answer 2

`(p^(-4)q^(5)r^(6))/(p^(-3)qr^(-2))=p^(-1)q^(4)r^(8)`

Explanation:

In division of powers with the same base, we must subtract the exponent of the denominator from the exponent of the numerator:

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

Then applying this to the problem:

`(p^(-4)q^(5)r^(6))/(p^(-3)qr^(-2))=p^(-4-(-3))q^(5-1)r^(6-(-2))`

Eliminating the parentheses:

`(p^(-4)q^(5)r^(6))/(p^(-3)qr^(-2))=p^(-4+3)q^(5-1)r^(6+2)\\ (p^(-4)q^(5)r^(6))/(p^(-3)qr^(-2))=p^(-1)q^(4)r^(8)`