Question

(3^4*3^-5)/3^-1
Pls help with my home work and also pls explain

Answer 1

Answer:

6561

Step-by-step explanation:

(3^4*3^-5)/3^-1

= 81*-243/-3

= -19683/-3

= 6561

Answer 2

Answer:

1

Step-by-step explanation:

(3⁴ × 3⁻⁵)/3⁻¹

3⁻⁵ = 1/3⁵

3⁻¹ = 1/3

now,

(3⁴ × 1/3⁵)/1/3

= (3 × 3 × 3 × 3/3×3×3×3×3) × 3 (all3 in the bracket will be cancelled except one 3 in the denominator)

= 3/3 = 1

Alternate method

(3⁴ × 3⁻⁵)/3⁻¹

as we know when the base is the same and the numbers are in multiplication, we can add power

∴ 3⁴⁺⁽⁻⁵⁾/3⁻¹ = 3⁴⁻⁵/3⁻¹ = 3⁻¹/3⁻¹

as we know when the base is the same and the numbers are in the division, we can subtract power

∴ 3⁻¹ ⁻⁽⁻¹⁾ = 3⁻¹⁺¹ = 3⁰

as we know that any number raise to the power 0 results in 1

∴ 3⁰ = 1