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Simplification of
Step 1: Rewrite
and
:
Step 2: Multiply the two expressions:
Step 3: Simplify:
Thus, the simplified form is:
Simplification of
Step 1: Rewrite
:
Step 2: Substitute:
Step 3: Simplify:
Thus, the simplified form is:
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Bonus Knowledge
To tackle these equations, you’ll often want to express everything using the same base to simplify each term effectively. For part (a), start by rewriting
as
and you will quickly notice how like terms can be combined. This same principle extends to the other equations, where recognizing the various expressions as powers of 3, 2, or other base numbers can streamline your calculations.
In part ©’s simplification, remember that
is equal to
. With such transformations, you can balance out both sides of the equation and eventually factor the equation down to a simpler form. This approach will yield clearer insights into how the terms relate to each other, making it easier to derive the desired result.