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.
