Write 16 × 8^(2x) as a power of 2 in terms of x
Aim: Our answer should be written in the form 2a+bx where a and b are constants that we are trying to find.
Firstly, we can write 16 in terms of a power of 2: 16 = 42 = 4 x 4 = (2 x 2) x (2 x 2) = 24
Similarly, 8 can be written as a power of 2: 8 = 2 x 4 = 2 x 2 x 2 = 23
Putting this together, we get: 16 x 82x = 24 x (23)2x
Using rules of indices: (23)2x = 23 x 2x = 26x
Hence, 16 × 82x = 24 x 26x = 24+6x
SL
Related Maths GCSE answers
All answers ▸There are 6 orange sweets and n total sweets in a bag. The probability of picking two sweets one at a time randomly and both being orange is 1/3. Show that n^2 - n - 90 = 0
A box contains an assortment of 100 coloured marbles, coloured red, blue and green. The ratio of blue balls to green balls is 1:3. If there are 16 red balls in the box, what is the ratio of red balls to green balls, and red balls to blue balls?
(x+3)(x-4)(x+5) is identical to x^3 +ax^2 -17x+b. Find the value of a and the value of b.
A cycle race is 3069.25 miles. Juan travels at a speed of 15.12 miles per hour. He cycles for 8 hours a day. Estimate how many days Juan will take to complete the race.