Video Transcript
Evaluate 64 over 16 cubed to the
negative one-half power.
We have this expression 64 over 16
cubed to the negative one-half power. And just like any operation, we’ll
begin inside the parentheses. Inside the parentheses, we have
this fraction 64 over 16. And before we do anything else, we
can reduce 64 over 16. They’re both divisible by
eight. 64 divided by eight is eight. 16 divided by eight is two. And eight over two equals four. This means, in our expression, in
place of 64 over 16, we can substitute four so that we now have an expression that
says four cubed to the negative one-half power.
And so, our next step will be in
order of operations to solve the exponent value four cubed. Four times four is 16 and 16 times
four is 64. In our expression, in place of four
cubed, we substitute 64. And now, we need to solve for the
negative one-half power. We know that 𝑎 to the negative 𝑥
power is equal to one over 𝑎 to the 𝑥 power.
We can then rewrite our expression
to be one over 64 to the positive one-half power. We know the one-half power is the
square root. So, we have one over the square
root of 64. The square root of 64 is eight. And that means this expression is
equal to one over eight.
