Video: Computing Numerical Expressions Using Laws of Exponents

4 × (3 × (3/4)⁴ − 0.75² − (11 × 3²)/(2⁴ × 4²))² = _.

05:48

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.

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