Video Transcript
Calculate the value of 5.96 multiplied by 10 to the power of five plus 6.04 multiplied by 10 to the power of six divided by 7.9 multiplied by 10 to the power of negative six, giving your answer in standard form.
Recall that a number written in scientific notation, also known as standard form, is written 𝑎 multiplied by 10 to the power of 𝑛, where the absolute value of 𝑎 must be greater than or equal to one and less than 10 and 𝑛 must be an integer.
In this question, we have a fraction made up of numbers written in scientific notation. We need to add the two numbers in the numerator and then divide by the denominator. First, to do the addition, 5.96 multiplied by 10 to the power of five plus 6.04 multiplied by 10 to the power of six, we must rewrite the expression so that both numbers have the same power of 10.
For positive powers, it is usually easier to rewrite the one with the higher power in terms of the one with the lower power. Therefore, we rewrite 6.04 multiplied by 10 to the power of six as 6.04 multiplied by 10 multiplied by 10 to the power of five, which is equal to 60.4 multiplied by 10 to the power of five. We can then take out the shared factor of 10 to the power of five, giving us 5.96 plus 60.4 multiplied by 10 to the power of five. This in turn is equal to 66.36 multiplied by 10 to the power of five. Whilst this is not written in standard form, as the value of 𝑎 is greater than 10, we will leave the answer in this form for the time being.
Returning to the original calculation, we now need to divide this by 7.9 multiplied by 10 to the power of negative six. We begin by rewriting the expression as the multiplication of two fractions and simplify each one separately. 66.36 divided by 7.9 is equal to 8.4. Recalling the quotient rule for exponents, 10 to the power of five divided by 10 to the power of negative six is equal to 10 to the power of 11, since five minus negative six equals 11. Since 8.4 lies between one and 10, this number is in standard form. And we conclude that the value of the given expression is 8.4 multiplied by 10 to the power of 11.
