Video Transcript
Simplify 𝑥 raised to the power of
negative two divided by 𝑥 raised to the power of negative four.
In this question, we are asked to
simplify an expression involving the quotient of bases raised to negative integer
exponents. To answer this question, we can
start by noting that bases in both expressions are the same. So we can see that this expression
is in the form of the quotient rule for exponents. This tells us that 𝑏 raised to the
power of 𝑚 over 𝑏 raised to the power of 𝑛 is equal to 𝑏 raised to the power of
𝑚 minus 𝑛.
In other words, we can evaluate the
quotient of two exponential expressions with the same base by raising the base to
the difference in their exponents. To apply this rule to our
expression, we set 𝑏 equal to 𝑥, 𝑚 equal to negative two, and 𝑛 equal to
negative four. This gives us 𝑥 raised to the
power of negative two minus negative four.
We can then evaluate the expression
in the exponent. We have that negative two minus
negative four is equal to negative two plus four, which we can calculate is equal to
two. Hence, we have shown that 𝑥 raised
to the power of negative two divided by 𝑥 raised to the power of negative four is
equal to 𝑥 squared.
