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skelet666 [1.2K]
2 years ago
13

Simplify the expression using the rules for

Mathematics
2 answers:
kodGreya [7K]2 years ago
7 0

Answer:

<em>( b^5 c^5 ) / a^10 </em>

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}  }

german2 years ago
6 0

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

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