Question

Multiply or divide as indicated. Leave your answer with no factors in the denominator. p⁻⁴q⁵r⁶/p⁻³qr⁻²

Answer 1

Answer:
`(q^4r^8)/(p)`

Explanation:

By the Negative exponent rule, we know that:

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

By the Quotient of powers property, we know that:

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

And by the Product of powers property, we know that:

`(a^m)(a^n)=a^((m+n))`

Applying this properties, we get:

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

Answer 2

`p^(-1)q^(4)r^(8)`.

Explanation:

The given expression is
`(p^(-4)q^5r^6)/(p^(-3)qr^(-2))`.

Recall and use the following rule of exponents;

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

We apply this rule to obtain:

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

`p^(-4+3)q^(4)r^(6+2)`.

This simplifies to:

`p^(-1)q^(4)r^(8)`.

Since we do not want to leave any factor in the denominator, the required answer is:

`p^(-1)q^(4)r^(8)`.