Question

1) 2+9х=4х+3 2) (9^-4)^2 / 9^-10

Answer 1

1) 2+9x=4x+3
    9x-4x=3-2
    5x=1
    x=1/5
    x= 0.2
2) $(9^{-4})^2$ / $9^{-10}$ =
  = $9^{-8}$ / $9^{-10}$ =
= $9^{-8-(-10)}$ =
= $9^{2}$ = 81

Answer 2

To solve the equation 1 + 2 * 9x = 4x + 3 + 2 + (9^-4)^2 / 9^-10, we'll follow the order of operations (also known as PEMDAS or BODMAS) to simplify and solve the equation step by step.

Step 1: Simplify the expression on the right-hand side

On the right-hand side of the equation, we have (9^-4)^2 / 9^-10. Let's simplify this expression first.

First, let's calculate the values inside the parentheses: (9^-4)^2. The negative exponent means we need to take the reciprocal of 9^4, so (9^-4)^2 becomes (1/9^4)^2.

Simplifying further, (1/9^4)^2 is equal to 1/9^(4*2), which is 1/9^8.

Now, let's simplify the denominator 9^-10. Similar to above, we take the reciprocal of 9^10, so 9^-10 becomes 1/9^10.

Now, we can rewrite the expression as (1/9^8) / (1/9^10).

To divide by a fraction, we multiply by its reciprocal. So, (1/9^8) / (1/9^10) is the same as (1/9^8) * (9^10/1).

Simplifying, we get 9^10/9^8, which is equal to 9^(10-8), which simplifies to 9^2.

Therefore, the expression (9^-4)^2 / 9^-10 simplifies to 9^2.

Step 2: Substitute the simplified expression back into the equation

Now that we have simplified the right-hand side of the equation, we can substitute it back into the original equation: 1 + 2 * 9x = 4x + 3 + 2 + 9^2.

Step 3: Simplify and solve the equation

Let's simplify the equation further:

1 + 2 * 9x = 4x + 3 + 2 + 9^2.

Multiplying 2 and 9x, we get 18x:

1 + 18x = 4x + 3 + 2 + 9^2.

Combining like terms on the right-hand side, we have:

1 + 18x = 4x + 14.

Now, let's isolate the variable x. Subtract 4x from both sides of the equation:

1 + 18x - 4x = 4x - 4x + 14.

This simplifies to:

1 + 14x = 14.

Subtract 1 from both sides:

1 + 14x - 1 = 14 - 1.

Simplifying further:

14x = 13.

Finally, divide both sides by 14 to solve for x:

14x/14 = 13/14.

The final solution is:

x = 13/14.

So, the solution to the equation 1 + 2 * 9x = 4x + 3 + 2 + (9^-4)^2 / 9^-10 is x = 13/14.