Question

Simplify the expression using the rules for

exponents.
Write your answer without negative exponents.

Answer 1

( b^5 c^5 ) / a^10

Explanation:

Properties of exponent we are going to use:

First step:
`a^(-1)` =
`(1)/(a)`

Second step:
`a^(n) b^(n)` =
`(ab)^(n)`

Third step:
`a^(m) a^(n)` =
`a^(m+n)`

Forth step:
`( a^(m) )^(n)` =
`a^(mn)`

~~~~~~~~~~~~~

1).
`(( ab^(-3) c^(-3) ) ^(5) )/((a^(-3) b^(4) c^(4) ) ^(-5) )` =
`( a b^(-3) c^(-3) ) ^(5) ( a^(-3) b^4 c^4 ) ^(5)`

2).
`( aa^(-3) b^(-3) b^(4) c^(-3) c^(4) ) ^(5)`

3).
`( a^(1-3) b^(-3+4) c^(-3+4) ) ^(5)`

4).
`a^(-2*5) b^(5) c^(5)`

`a^(-10) b^(5) c^(5)` =
`(b^5 c^5 )/(a^(10) )`

Answer 2

Explanation:

(a×b^-3×c^-3)⁵ / (a^-3×b⁴×c⁴)^-5

let's look at the numerator (the top) first :

a⁵×b^-15×c^-15

and now the denominator (the bottom) :

a¹⁵×b^-20×c^-20

both divided are (due to the commutative rules of multiplication we can split this first into the parts of the individual variables, and then multiply them all with each other) :

a⁵/a¹⁵ = 1/a¹⁰

b^-15 / b^-20 = b^(-15 ‐ -20) = b⁵

c^-15 / c^-20 = c⁵

so we get as result :

b⁵c⁵/a¹⁰