Simplify (4x^10)^20/(8x^20)^10

Question

Simplify (4x^10)^20/(8x^20)^10

Answer

STEP 1:   Observe the given term:The terms in the numerator and denominator are powers raised to some other power. For simplifying the given expression, you first need to simplify the numerator and denominator and then cancel any common factors.

Take the numerator. It can be simplified using the law:

                                         (aⁿb^m)^p = a^npb^mp


Raise each factor to the power 20.
STEP 2:    By following a similar method, you can get a simplified expression in the denominator also.

Since the term x²⁰⁰ is common to both the numerator and denominator, you can choose to cancel it out in the next step.
STEP 3:    Note that the base of the term in the numerator is 4, and that in the denominator is 8. Further simplification can be possible only if we make both the bases same.

Express the numerator and the denominator as powers of 2.STEP 4:    Again, simplify using the law of exponents,
          (a^m)ⁿ = a^mn.This gives:


STEP 5: Apply the quotient rule for exponents,
This gives:
The given expression thus simplifies to 2¹⁰ or 1024.