Question

Solve the following using laws of exponent.
a) (-5/9)-² × (-3/5)-³ × (3/5)^-0
b) {(-3/7)²}-³
c) {(-7/9)-³ × (-9/7)-³}÷(-7/9)-³
d) (5-² × 2-²) × 10²
e) (-3/2)-⁴ × (-3/2)
f) {(-1/3)-⁴ ÷ (-1/3)^-5}³
Please help me.​

Answer 1

Answer:

Here are some solved examples on exponents using the laws of exponents.

1. Evaluate the exponent:

(i) 5-3

(ii) (1/3)-4

(iii) (5/2)-3

(iv) (-2)-5

(v) (-3/4)-4

We have:

(i) 5-3 = 1/53 = 1/125

(ii) (1/3)-4 = (3/1)4 = 34 = 81

Here are some solved examples on exponents using the laws of exponents.

1. Evaluate the exponent:

(i) 5-3

(ii) (1/3)-4

(iii) (5/2)-3

(iv) (-2)-5

(v) (-3/4)-4

We have:

(i) 5-3 = 1/53 = 1/125

(ii) (1/3)-4 = (3/1)4 = 34 = 81

Step-by-step explanation:

Solution:

(-2/7)-4 × (-5/7)2

= (7/-2)4 × (-5/7)2

= (-7/2)4 × (-5/7)2 [Since, (7/-2) = (-7/2)]

= (-7)4/24 × (-5)2/72

= {74 × (-5)2}/{24 × 72 } [Since, (-7)4 = 74]

= {72 × (-5)2 }/24

= [49 × (-5) × (-5)]/16

= 1225/16

3. Evaluate: (-1/4)-3 × (-1/4)-2

Solution:

(-1/4)-3 × (-1/4)-2

= (4/-1)3 × (4/-1)2

= (-4)3 × (-4)2

= (-4)(3 + 2)

= (-4)5

= -45

= -1024.

4. Evaluate: {[(-3)/2]2}-3

Solution:

{[(-3)/2]2}-3

= (-3/2)2 × (-3)

= (-3/2)-6

= (2/-3)6

= (-2/3)6

= (-2)6/36

= 26/36

= 64/729

5. Simplify:

(i) (2-1 × 5-1)-1 ÷ 4-1

(ii) (4-1 + 8-1) ÷ (2/3)-1

Solution:

(i) (2-1 × 5-1)-1 ÷ 4-1

= (1/2 × 1/5)-1 ÷ (4/1)-1

= (1/10)-1 ÷ (1/4)

= 10/1 ÷ 1/4

= (10 ÷ 1/4)

= (10 × 4)

= 40.

(ii) (4-1 + 8-1) ÷ (2/3)-1

= (1/4 + 1/8) ÷ (3/2)

= (2 + 1)/8 ÷ 3/2

= (3/8 ÷ 3/2)

= (3/8 ÷ 2/3)

= 1/4