Question Video: Simplifying Algebraic Expressions Using Laws of Exponents Mathematics • 9th Grade

Simplify โˆ’(12๐‘ฅโถ๐‘ฆโต/6๐‘ฅโด๐‘ฆ).


Video Transcript

Simplify negative 12๐‘ฅ raised to the sixth power ๐‘ฆ raised to the fifth power all divided by six ๐‘ฅ raised to the fourth power ๐‘ฆ.

In this question, we are asked to simplify the quotient of two expressions involving unknown values of ๐‘ฅ and ๐‘ฆ. The first thing we can note about the given expression is that both the numerator and denominator are monomials, since they are the product of constants and variables where the variables are raised to nonnegative integer exponents.

When finding the quotient of monomials, we want to divide each of the shared factors separately. We can do this directly in the given expression, or we can rewrite the expression to separate these factors. It is not necessary to rewrite the expression in this form. However, it can be useful to see how the division occurs.

We can now evaluate each of these divisions separately. First, we can calculate that negative 12 over six is equal to negative two. For the next two quotients, we can note that we are dividing exponential expressions with the same base. So we can simplify this by recalling that the quotient rule for exponents tells us that for a nonzero base ๐‘, ๐‘ raised to the power of ๐‘š over ๐‘ raised to the power of ๐‘› is equal to ๐‘ raised to the power of ๐‘š minus ๐‘›. In other words, when taking the quotient of two exponential expressions with the same base, we can instead raise the base to the difference in the exponents.

Assuming that ๐‘ฅ and ๐‘ฆ are not equal to zero and applying this to the final two quotients gives us ๐‘ฅ raised to the power of six minus four and ๐‘ฆ raised to the power of five minus one, respectively. Evaluating the expression in each of the exponents gives us negative two times ๐‘ฅ squared multiplied by ๐‘ฆ to the fourth power, provided ๐‘ฅ and ๐‘ฆ are nonzero.

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