In November, Hillary drove 580 miles in her car. The car traveled 33.5 miles for each gallon of petrol used. Petrol costs £1.09 per litre.

1 gallon = 4.55 litres.

Work out the costs of the petrol the car used in November.

Step-by-step explanation:

First we divide the number of miles Hillary drove in November by the number of miles per gallon to figure out how many gallons of petrol she used.

580/33.5 = about 17.3 gallons of petrol

Next, we multiply the gallons of petrol by a liters to figure out how many liters she used.

17.3 x 4.55 = about 78.8 litres

Finally, we multply the number of litres Hillary used by the cost per litre

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.