9514 1404 393
Answer:
(C) x^38
Explanation:
The explanation speaks for itself. It is a restatement of the Order of Operations as it applies to this expression.
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Written in plain text, the expression is ...
((x^6·x^10)/(x^-3))^2
The order of operations requires you evaluate the inner parentheses first. The exponential terms cannot be simplified, so you perform the product. The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
So, you now have ...
((x^(6+10))/(x^-3))^2 = (x^16/x^-3)^2
Again, you perform the division inside parentheses before anything else. The applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
So, you have ...
(x^(16-(-3)))^2 = (x^19)^2
Now, you can perform the exponentiation. The applicable rule of exponents is ...
(a^b)^c = a^(bc)
So, the final simplification is ...
(x^19)^2 = x^(19·2) = x^38
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Comment on exponent rules
The rules of exponents follow directly from the fact that an exponent is a representation of repeated multiplication.
Product rule:
(x^2)(x^3) = (x·x)(x·x·x) = x·x·x·x·x = x^(2+3) = x^5
Quotient rule:
(x^3)/(x^2) = (x·x·x)/(x·x) = x = x^(3-2) = x^1
Power rule:
(x^3)^2 = (x·x·x)^2 = (x·x·x)(x·x·x) = x^(3·2) = x^6