Solution:

To find the value of x, we need to simplify the expression step by step.

Simplification:

(-8/9)¹⁵ ÷ (-8/9)

= (-8/9)¹⁵ × (-9/8)

= -8¹⁵ × 9⁻¹⁵ × 9⁻¹

= -8¹⁵ × 9⁻¹⁶

= - (8/9)¹⁵

Now, we need to compare the value of x with (8/9)² and check if they are equal or not.

Comparison:

x = - (8/9)¹⁵

(8/9)² = 64/81

We can see that x is negative and (8/9)² is positive. Therefore, they are not equal.

Explanation:

The given expression can be simplified using the laws of exponents. We can use the rule that states that when we divide two powers with the same base, we can subtract their exponents. We can also use the rule that states that when we raise a fraction to a negative power, we can flip the fraction and raise it to the positive power.

After simplifying the expression, we can compare the value of x with the value of (8/9)². We can see that they are not equal. This means that the expression (-8/9)¹⁵ ÷ (-8/9) is not equal to (8/9)².

Final Answer:

x = - (8/9)¹⁵

They are not equal.

X=13