# Question Video: Solving Exponential Equations Using Laws of Exponents Mathematics • 10th Grade

Solve 5^π₯ Γ 6^(βπ₯) = 25/36.

01:25

### 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.