Video Transcript
Solve five to the power of π₯ multiplied by six to the power of negative π₯ is equal
to 25 over 36.
In order to answer this question, we need to recall some of our laws of
exponents. π to the power of negative π₯ is equal to one over π to the power of π₯. This means that we can rewrite the left-hand side of our equation as five to the
power of π₯ multiplied by one over six to the power of π₯. This in turn simplifies to five to the power of π₯ over six to the power of π₯. This is equal to 25 over 36.
Another of our laws of exponents states that π to the power of π₯ divided by π to
the power of π₯ is equal to the fraction π over π all raised to the power of
π₯. This means that the left-hand side of our equation can be rewritten as five-sixths to
the power of π₯. As five squared is equal to 25 and six squared is equal to 36, the right-hand side
can be rewritten as five-sixths squared.
Our base numbers are now the same, which means the exponents must be equal. The solution to the equation five to the power of π₯ multiplied by six to the power
of negative π₯ equals 25 over 36 is π₯ equals two.
