please question number 2 d and e and question number 3 full solve please
Answers
Step-by-step explanation:
for question 2 d)
(-2/5)^2*(-2/5)^3 = (-2/5)^2+3
explanation :
the math rule( first rule) for this type of equation is that since the denominators (5) are the same and the numerators (-2) are the same the same values will be used for the answer.
in order to solve the powers . take this formula into account ( if the constants (a) are the same
a^2 * a^3 = a^2+3
this is because with multiplication we add the powers
and if this was with division eg : a^2 / a^3 = a^2-3
we would subtract the powers.
therefore in this case: the values of (-2/5) is the same and the equation uses multiplication . hence add the powers to get the final answer
it would be (-2/5)^2*(-2/5)^3 = (-2/5)^2+3
for question 2 e)
the math rule that is used for this equation is that :
(a^b)^c = a ^b*c
therefor use this rule to get the answer :
(10^5)^3 = 10^(5+3)
question number 3 a)
equation: (18/35)^19 / (18/35)^19
recall the math rule : the math rule( first rule) for this type of equation is that since the denominators (35) are the same and the numerators (18) are the same the same values will be used for the answer.
now lets solve the powers : since the equation makes use of a division , recall that you need to subtract the powers --- a^19 / a^19 = a^19-19
now that we have found that the answer is a ^0 ... the math rule also states if the answer is a^0 then the final answer = 1
heres an example : 5^0 = 1 ( you can type this on the calculator to verify)
therefore the answer for this equation ( (18/35)^19 / (18/35)^19 ) = 1
question number 3 b)
the equation is : (7^0 + 3^0) * ( 8^0 - 5^0)
recall the math rule if a^0 then answer = 1
therefore : 7^0 =1
: 3^0= 1
:8^0 = 1
: 5^0 = 1
insert these into the origional formula :
(1+ 1) * (1-1) =
(2)*(0) solve this
and this is equal to 0
answer for this equation is 0
question number 3 d)
the equation is ((-3/4)^5 * (-3/4)^3) / (9/16)^4
for this equation make use of bodmas ( brackets of division multiplication addition and subtraction) first :
solve what is in brackets :
((-3/4)^5 * (-3/4)^3)
recall the rule : the math rule( first rule) for this type of equation is that since the denominators (4) are the same and the numerators (-3) are the same the same values will be used for the answer.
now to solve the powers: recall the rule : since the equation uses multiplication you add the powers ( as both denominators and numerators are the same)
a^5 * a^3 = a^5+3
this gives us a^8
the overall answer would be : (-3/4)^8
now to solve the second part ( make use of the first parts answer:
(-3/4)^8 / (9/16)^4
first we can recognise that the numer ator and denominators are not the same . therefore use the math rule
if (a/b) / (c/d)
then use the reciprocal of (c/d) meaning:
(a/b) * (d/c)
this rule can be used for the equation :
(-3/4)^8 / (9/16)^4
becomes
(-3/4)^8 * (16/9)^4 this can be simplified to :
(-1/1)^8 * (4/3)^4
= this is done by crossing out the multiplies of the numbers : 16 /4 = 4
now multiply -1 * 4 = -4
and 1*3 = 3
which is equal to -4/3
now solve the powers . since multiplication is used add the powers = 8+ 4 = 12
answer for this equation = (-4/3 )^12
question number 3 e)
first separate the equation into two parts :
((-3/4)^4 * 125/27) ---- part 1
and ((5/3)^2 *9/16) --- part 2
lets solve the first part :
((-3/4)^4 * 125/27)
in order to get rid of the power
use rule :
therefore : (-3)^4 / 4^4 this is equal to 81/256
now solve the second part :
((5/3)^2 *9/16)
get rid of the power us the same rule : (a/b)^c = a^c / b^c
therefore : 5^2 / 3^2 which is equal to 25 /9
now solve the entire equation substituting those new values :
(81/256) / (25 /9)
in order to simplify use reciprocal to get rid of division as well :
81/256 * 9/25
simplify this by cancelling out multiples :
since they can not be simplified as no multiples... just multiply the values :
81*9 =729 and 256 *25 =6400
your answer = 729/6400
hope these explanations help you understand how to approach the question.... :)