Can someone please help me with this

9514 1404 393

  (C)   x^38

Step-by-step 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

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

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step-by-step explanation: