Question Video: Simplifying an Algebraic Expression Using Exponent Laws | Nagwa Question Video: Simplifying an Algebraic Expression Using Exponent Laws | Nagwa

Question Video: Simplifying an Algebraic Expression Using Exponent Laws Mathematics • First Year of Preparatory School

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Simplify (−(𝑥/𝑦))⁻³ × (−(𝑥/𝑦))².

02:14

Video Transcript

Simplify negative 𝑥 over 𝑦 all raised to the power of negative three multiplied by negative 𝑥 over 𝑦 all squared.

In this question, we are asked to simplify an expression involving the product of bases raised to different exponents. To answer this question, we first need to note that the bases in both of the factors are the same. We can then note that this expression is in the form of the product rule for exponents. We can recall that this tells us that 𝑏 to the power of 𝑚 times 𝑏 to the power of 𝑛 equals 𝑏 to the power of 𝑚 plus 𝑛. In other words, we can multiply exponential expressions of the same base by raising the base to the sum of the exponents.

Applying this result with the base 𝑏 equal to negative 𝑥 over 𝑦, 𝑚 equal to negative three, and 𝑛 equal to two gives us negative 𝑥 over 𝑦 all raised to the power of negative three plus two. We can then evaluate the expression in the exponent to obtain negative 𝑥 over 𝑦 all raised to the power of negative one.

It is worth noting that we can simplify further by recalling that raising a base to the power of negative one is equivalent to taking the reciprocal of the base. So, 𝑎 over 𝑏 all raised to the power of negative one is equal to 𝑏 over 𝑎. We can calculate that the reciprocal of negative 𝑥 over 𝑦 is negative 𝑦 over 𝑥. So we could simplify this expression further to obtain negative 𝑦 over 𝑥. However, we can also leave our answer as negative 𝑥 over 𝑦 all raised to the power of negative one.

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