can someone help me solve this with working
Answers
Answer:
1.i) (4^3)^-1= 64^-1
=1/64
ii) (1/2)^-5=2^5
=32
iii) (4/3)^3=(3/4)^3
=27/64
iv) (-3)^-4= (1/-3)^4
=1/81
v) (-2/3)^-5= (3/-2)^5
= 243/32
2.i) (-2/3)^2×-2
= (-2/3)^-4
= (3/-2)^4
= 81/32
ii) (-1/3)^2×-2×-1
= (-1/3)^4
= 1/81
iii)(3/2)^2×-2
= (3/2)^-4
= (2/3)^4
= 32/81
3. {(3)^3-(2)^3}÷(4)^3
= (27-8)÷ 4^3
= 19÷64
= 19/64
4. (3/4-4)^-1
= (3/4-16/4)^-1
= (-13/4)^-1
= -4/13
5. (5×3)^-1÷6^-1
= 15^-1÷6^-1
= (15/6)^-1
= (5/2)^-1
= 2/5
6. -4+(-5)= 3x ( since, bases are equal therefore power will also be equal)
= -4-5=3x
= -9=3x
= x= -9/3
= x= -3
7. 4+(-7)= 2x-1 (since, bases are equal therefore power will also be equal)
= 4-7=2x-1
= -3+1= 2x
= x=-2/2
= x= -1
8.Let the number be x.
therefore, x × (-6)-1= 9^-1
= x= (9/-6)^-1
= x= (3/-2)^-1
= x= -2/3
9. let the no. be x .
therefore, (-2/3)^-3÷x=(4/27)^-2
= (3/-2)^3÷x= (27/4)^2
= 27/-8÷x= 729/16
= x= 729/16×-8/27
= x= -27/2
10. 5^2x+1÷5^2= 5^3
= 2x+1-2=3 (since, bases are equal therefore power will also be equal)
= 2x-1=3
= 2x= 3+1
= x=4/2
= x= 2