Question

Answer the following

Answer 1

Answer:

solution

Step-by-step explanation:

• 9^m ÷3 ^-2 = 9 ^4
• 9^m ÷ 1/3^2 = 9 ^4
• 9^m ÷ 1/9 = 9^4
• If any thing is in divide if we reciprocal it then it converted into multiplication.
• 9^m × 9 = 9^ 4
• 9^ m × 9 = 9×9×9×9
• 9^ m = 9×9×9
• 9^ m = 9^3
• bases are equal then powers are equal
• so, m= 3

Answer 2

Answer:

3

Step-by-step explanation:

(I will substitute 'm' to 'x')

9ˣ ÷ 3⁻² = 9⁴

= 9ˣ = (9⁴) x (3⁻²)

= 9ˣ = 6561 x 1 / 3²        [using property - x⁻ⁿ = 1 / xⁿ ]

= 9ˣ = 6561 x 1 / 9

= 9ˣ = 6461 / 9

= 9ˣ = 729

As we know that 729 = 9³

∴ 9ˣ = 9³

So Therefore x = 3