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

Solve 5^๐‘ฅ ร— 6^(โˆ’๐‘ฅ) = 25/36.

01:25

Video Transcript

Solve five to the power of ๐‘ฅ multiplied by six to the power of negative ๐‘ฅ is equal to 25 over 36.

In order to answer this question, we need to recall some of our laws of exponents. ๐‘Ž to the power of negative ๐‘ฅ is equal to one over ๐‘Ž to the power of ๐‘ฅ. This means that we can rewrite the left-hand side of our equation as five to the power of ๐‘ฅ multiplied by one over six to the power of ๐‘ฅ. This in turn simplifies to five to the power of ๐‘ฅ over six to the power of ๐‘ฅ. This is equal to 25 over 36.

Another of our laws of exponents states that ๐‘Ž to the power of ๐‘ฅ divided by ๐‘ to the power of ๐‘ฅ is equal to the fraction ๐‘Ž over ๐‘ all raised to the power of ๐‘ฅ. This means that the left-hand side of our equation can be rewritten as five-sixths to the power of ๐‘ฅ. 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 ๐‘ฅ multiplied by six to the power of negative ๐‘ฅ equals 25 over 36 is ๐‘ฅ equals two.

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