Question

Simplify and express the Solution in the positive exponent form:

`("a"^-7 xx "b"^-7 xx "c"^5 xx "d"^4)/("a"^3 xx "b"^-5 xx "c"^-3 xx "d"^8)`

Answer 1

`("a"^-7 xx "b"^-7 xx "c"^5 xx "d"^4)/("a"^3 xx "b"^-5 xx "c"^-3 xx "d"^8)`

We will use the following rules of exponents:

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

2. a^m × aⁿ = a^m+n

3. For any negative exponent `a^-n = 1/a^n`

For a: `a^-7/a^3 = a^(-7-3) =a^-10`

For b: `b^-7/b^-5 = b^(-7+5) = b^-2`

For c: `c^5/c^-3 = c^(5+3) = c^8`

For d: `d^4/d^8 = d^(4-8) = b^-4`

Now, combine all the simplified terms: a⁻¹⁰ × b⁻² × c⁸ × d⁻⁴

We can rewrite terms with negative exponents as fractions:

`1/a^10 xx 1/b^2 xx c^8 xx 1/d^4`

This gives

`c^8/(a^10 xx b^2 xx d^4)`