Question

The power generated by a wind turbine depends on the wind speed . The expression 800 v^3 gives the power in watts for a certain wind turbine at wind speed v in meters per second . If the wind speed triples , by what factor does the power generated by the wind turbine increase ?

2) Can you write the expression 49x^2y^2z^2 using only one exponent ? Show how or explain why not ?

Answer 1

1. it would increase by 27 times
in other words, 3^3 times

2. You can rewrite the expression using one exponent because each variable is being squared and multiplied by each other
if you had 3^2 x 4^2 it would be 144 (9 x 16)
same as if you had (3 x 4)^2 which is 12^2, which is also 144
the expression would be (7xyz)^2

Answer 2

Power  = 800v³

If the speed triples, v is replaced by 3v.

  Power = 800*(3v)³ =  800*27v³ = 27*(800v³)

 The power increases by 27 times.


2)  49x²y²z² 

The expression can be written using one exponent

49x²y²z² = 7²* x² *y² * z²   = (7xyz)²

                                                 =  (7xyz)²