Video Transcript
Four multiplied by three multiplied
by three-quarters to the power of four minus 0.75 squared minus 11 multiplied by
three squared divided by two to the power of four multiplied by four squared all
squared is equal to blank.
In order to work out the answer to
this calculation, we’ll, firstly, look at the three separate parts inside the large
parentheses. The first of these three parts is
three multiplied by three-quarters to the power of four. If we wish to raise a fraction to
any power, we can split the numerator and denominator such that 𝑎 over 𝑏 to the
power of 𝑛 is equal to 𝑎 to the power of 𝑛 divided by 𝑏 to the power of 𝑛.
This means that three-quarters to
the power of four is the same as three to the power of four divided by four to the
power of four. Three to the power of four is the
same as three multiplied by three multiplied by three multiplied by three. As three multiplied by three is
equal to nine, this is the same as nine multiplied by nine. This gives us 81. Three to the power of four equals
81.
We can calculate four to the power
of four in the same way. Four multiplied by four equals
16. So, we need to multiply 16 by
16. This is equal to 256. As 16 multiplied by 10 is 160. And, 16 multiplied by six is
96. Three multiplied by three-quarters
to the power of four is equal to three multiplied by 81 over 256. Three is the same as three over
one. And, we can multiply two fractions
by timesing the numerators and timesing the denominators. Three multiplied by 81 is equal to
243. This means that the first part of
our calculation simplifies to 243 over 256.
The second part of our calculation
inside the parentheses was 0.75 squared. We know that 0.75 is the same as
three-quarters. So, we need to square this. Once again, we can square the
numerator and then square the denominator, separately. Three squared is equal to nine. And, four squared is equal to
16. Therefore, 0.75 squared is equal to
nine over 16 or nine sixteenths.
The final part of the calculation
inside the parentheses was 11 multiplied by three squared divided by two to the
power of four multiplied by four squared. Three squared is equal to nine, so
the numerator simplifies to 11 multiplied by nine. Two to the power of four is equal
to 16. And, four squared is also equal to
16. On the denominator, we have 16
multiplied by 16. 11 multiplied by nine is equal to
99. And, we’ve already worked out that
16 multiplied by 16 is 256.
We now have three fractions, two of
which have a denominator of 256. We can make the denominator of the
other fraction equal to 256 by multiplying by 16. Remember, whatever you do to the
bottom, you must do to the top. Nine multiplied by 16 is equal to
144. Therefore, nine over 16 is the same
as 144 over 256. We can now substitute all three of
these fractions back into the calculation.
Inside the bracket or parentheses,
we have 243 over 256 minus 144 over 256 minus 99 over 256. We need to square this and multiply
the answer by four. As the denominators are the same,
we just need to subtract the numerators. We need to subtract 144 and 99 from
243. 243 minus 144 is equal to 99. And, subtracting 99 from this gives
us zero. This means that we have zero over
256. Zero divided by any number is still
equal to zero. Squaring this and then multiplying
by four will still give us an answer of zero.
The answer to the calculation, four
multiplied by three multiplied by three-quarters to the power of four minus 0.75
squared minus 11 multiplied by three squared divided by two to the power of four
multiplied by four squared all squared, is zero.
