Video Transcript
Calculate 10 to the fifth power
multiplied by 25 squared multiplied by four divided by 20 squared multiplied by five
to the fifth power.
To calculate this expression, we
can write the powers in expanded form and then cancel common factors in the
numerator and denominator. The first term in the numerator, 10
to the fifth power, can be rewritten as 10 multiplied by 10 multiplied by 10
multiplied by 10 multiplied by 10. 25 squared can be written as 25
multiplied by 25. This means that the entire
numerator can be rewritten as shown.
We can do the same with the
denominator and rewrite 20 squared and five to the fifth power. Whilst we could cancel at this
stage, we can simplify our expression further by writing the numerator and
denominator as products of prime factors. We know that 10 is equal to two
multiplied by five. 25 can be rewritten as five
multiplied by five. We can rewrite four as two
multiplied by two. And 20 written as a product of
prime factors is two multiplied by two multiplied by five.
We can use the first three of these
to rewrite the numerator as shown. And repeating this process with the
denominator, we have the following expression. Next, we can cancel common
factors. Two multiplied by two multiplied by
two multiplied by two can be canceled from the numerator and denominator. We can also cancel seven fives from
the numerator and denominator. Our expression therefore simplifies
to two multiplied by five multiplied by five multiplied by two multiplied by two all
divided by one. This is equal to two cubed
multiplied by five squared. And since two cubed is equal to
eight and five squared is 25, we have eight multiplied by 25, which is equal to
200. 10 to the fifth power multiplied by
25 squared multiplied by four divided by 20 squared multiplied by five to the fifth
power is 200.
