Question

find the values of the following using laws of exponents
a) (3⁰-2⁰)+3¹
b) (-5/8)³×(-5/8)⁷
c) 5⁸/125
d) {(2/3)²}³÷(2/3)⁶
e)(4/5)⁶÷(8/25)⁶
​

Answer 1

Answer:

a) 5

b) (-5/8)¹⁰

c) 3125

d) 1

e) (5/2)⁶

Step-by-step explanation:

a) a⁰=1

So, (3⁰-2⁰)+3¹ = 1+1 + 3

= 2+3 = 5

b) a^m + a^n = a^(m+n)

(-5/8)³×(-5/8)⁷ = (-5/8)^(3+7)

= (-5/8)¹⁰

c) a^m/a^n = a^(m-n)

5⁸/125 = 5⁸/ 5³

= 5^(8-3)

= 5^5

= 3125

d) (a^m)^n = a^(m×n)

{(2/3)²}³÷(2/3)⁶ = (2/3)⁶ ÷ (2/3)⁶

= (2/3)⁰

= 1

e) (4/5)⁶÷(8/25)⁶ = (2²/5)⁶÷ (2³/5²)⁶

(4/5)⁶÷(8/25)⁶ = (2¹²/5⁶) ÷ (2¹⁸/5¹²)

(4/5)⁶÷(8/25)⁶ = (2¹² × 5¹²) / (2¹⁸ × 5⁶)

(4/5)⁶÷(8/25)⁶ = 2^(-6) × 5⁶

(4/5)⁶÷(8/25)⁶ = 5⁶ / 2⁶ = (5/2)⁶

Mark my answer as brainliest.

Cheers!