Question

Simplify the expression using the rules for
exponents.
Write your answer without negative exponents.

Answer 1

Step-by-step 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

Answer 2

Answer:

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

Step-by-step explanation:

Properties of exponent we are going to use:

First step: $a^{-1}$ = $\frac{1}{a}$

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). $\frac{( ab^{-3} c^{-3} ) ^{5} }{(a^{-3} b^{4} c^{4} ) ^{-5} }$ = $( a b^{-3} c^{-3} ) ^{5} ( a^{-3} b^4 c^4 ) ^{5}$

2). $( aa^{-3} b^{-3} b^{4} c^{-3} c^{4} ) ^{5}$

3). $( a^{1-3} b^{-3+4} c^{-3+4} ) ^{5}$

4). $a^{-2*5} b^{5} c^{5}$

$a^{-10} b^{5} c^{5}$ = $\frac{b^5 c^5 }{a^{10} }$