# Question Video: Simplifying Rational Algebraic Expressions Using Laws of Exponents Mathematics

Simplify ((6^π¦) Γ (6^π¦) Γ (6^π¦) Γ (6^π¦) Γ (6^π¦) Γ (6^π¦))/((6^π¦) + (6^π¦) + (6^π¦) + (6^π¦) + (6^π¦) +(6^π¦)).

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### Video Transcript

Simplify six π¦ times six π¦ times six π¦ times six π¦ times six π¦ times six π¦ over six π¦ plus six π¦ plus six π¦ plus six π¦ plus six π¦ plus six π¦.

In other words, simplify six π¦ times itself six times over six π¦ plus itself six times. This is not as simple as it might look. We need to consider our exponent rules. If we multiply π₯ to the π power times π₯ to the π power, we get π₯ to the π power squared. We take a power of a power. We can apply this to our numerator. Instead of having six π¦ times itself six times, we can write six π¦ to the sixth power. This will be the new numerator, six π¦ to the sixth power.

The denominator is a little different. Consider π₯ to the π power plus π₯ to the π power. We say thatβs two π₯ to the π power. We have two π₯ to the π power terms. In our case, we have six six to the π¦ power terms. And we can break this up. We can say that divided by six is the same thing as multiplying by one-sixth. And then, weβll have six to the π¦ power to the sixth power over six to the π¦ power.

In the denominator, we could call six to the π¦ power six to the π¦ power to the first power. And that would cancel out one of the six to the π¦ power terms. Our numerator then becomes six to the π¦ power to the fifth power.

Okay, what can we say about this one over six? We can call it one over six to the first power. And weβre going to multiply that by six to the π¦ power to the fifth power. We can rewrite one over six to the first power as six to the negative one power. And we can take this power to a power six to the π¦ to the fifth power and rewrite it as six to the five π¦ power.

When final rule will help us with our simplification, when our exponents have the same base and theyβre being multiplied together, we add their exponents. We will have six to the negative one plus five π¦ power, which we could rewrite as six to the five π¦ minus one power.