Video Transcript
Calculate seven squared multiplied
by two to the power of four over 14 cubed.
To begin, we recall that exponents
represent repeated multiplication. So we can write seven squared as
seven times seven and two to the fourth power as two times two times two times two
and 14 cubed as 14 times 14 times 14. Since the numerator is written in
factors of seven and two, which are both factors of 14, we can try to write the
denominator in factors of seven and two. Each factor of 14 can be split into
factors of seven times two.
So we have a denominator with three
factors of seven and three factors of two. These factors can be written in any
order with or without parentheses, as multiplication is commutative and
associative. We notice that the numerator and
denominator have two common factors of seven, which we cancel. And we are left with one factor of
seven in the denominator. Next, we find three factors of two
in common and cancel those. And we are left with only one
factor of two in the numerator.
We have canceled all common factors
and have found the simplified value of our expression to be two-sevenths.
