Question

(9^–5)² ÷ (27)^–6 = ______.

पर्याय

• 9⁸

• 9

• `1/9`

• `1/27`

Answer 1

(9^–5)² ÷ (27)^–6 = `underlinebb(1/9)`.

Explanation:

We are asked to evaluate:

(9^–5)² ÷ (27)^–6

Step 1: Simplify (9^–5)²

Use the exponent rule (a^m)ⁿ = a^{m × n}:

(9^–5)² = 9^–10 

Step 2: Simplify (27)^–6

We know that 27 = 3³, so:

27^–6 = (3³)^–6 = 3^–18 

Step 3: Combine the two terms

Now, the expression becomes:

`9^-10/3^-18`

Recall that 9 = 3², so:

9^–10 = (3²)^–10 = 3^–20

Thus, the expression simplifies to:

`3^-20/3^-18`

Step 4: Apply the exponent rule for division

Using the property `a^m/a^n = a^(m - n)`, we get:

`3^(-20 - (-18)) = 3^(-20 + 18) = 3^-2`

Step 5: Simplify

`3^-2 = 1/3^2 = 1/9`

The value of the expression is `1/9`.