Simplify Complex Expression: (x^4⋅x^8⋅x^(-3))/(x^(-4)) ÷ (x^10⋅x^3)/x^5

Question

x4x8x3x4——x10x3x5 \frac{x^4x^8x^{-3}}{x^{-4}}_{——}\frac{x^{10}x^3}{x^5}

Video Solution

Solution Steps

00:00 Complete the sign
00:03 When multiplying powers with equal bases
00:07 The power of the result equals the sum of powers
00:11 We'll use this formula in our exercise, we'll sum the powers
00:18 We'll use the same method for the right side
00:27 Let's calculate the numerator's powers
00:35 When dividing powers with equal bases
00:38 The power of the result equals the difference of powers
00:42 We'll use this formula in our exercise, we'll subtract the powers
00:55 If the variable is negative, then the number will be negative
01:02 Since we don't know, we cannot determine
01:05 And this is the solution to the question

Step-by-Step Solution

To solve the problem, follow these steps to simplify both expressions using exponent rules:

First Expression: x4x8x3x4\frac{x^4 x^8 x^{-3}}{x^{-4}}

  • Combine the exponents in the numerator: x4+83=x9x^{4+8-3} = x^9.
  • Apply the quotient rule: x9x4=x9(4)=x9+4=x13\frac{x^9}{x^{-4}} = x^{9 - (-4)} = x^{9 + 4} = x^{13}.

Second Expression: x10x3x5\frac{x^{10} x^3}{x^5}

  • Combine the exponents in the numerator: x10+3=x13x^{10+3} = x^{13}.
  • Apply the quotient rule: x13x5=x135=x8\frac{x^{13}}{x^5} = x^{13-5} = x^8.

Now we compare the results:
First Expression: x13x^{13}
Second Expression: x8x^8

In general, x13x^{13} is larger than x8x^8 for positive x x , but since xx could be any real number not zero, the full comparison could vary for negative xx.
Therefore, given the context, it's difficult to calculate a single universal answer without more information on the value of xx.

Thus, it is not possible to calculate universally between these expressions.

Therefore, our answer is Choice 4: It is not possible to calculate.

Answer

It is not possible to calculate