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# If (9/7)^{3 }× (49/81)^{(2x-6)} = (7/9)^{9}, What is the value of x?

To prove this equation true we will use exponential power identity.

## Answer: If (9/7)^{3 }× (49/81)^{(2x-6)} = (7/9)^{9 }then value of x is 6

Here's the solution.

**Explanation:**

⇒ (9/7)^{3 }× (49/81)^{(2x-6)} = (7/9)^{9}

We can write (9/7)^{3 }as (7/9)^{-3}

⇒ (7/9) ^{-3 }× [ (7/9)^{2 }] ^{(2x-6)} = (7/9)^{9}

We know that x^{a }+ x^{b }= a + b

⇒ (7/9) ^{-3 }× (7/9) ^{(4x-12)} = (7/9)^{9 }

As we know that the base is same, so we can add the powers.

⇒ - 3 + 4 x - 12 = 9

⇒ 4 x - 15 = 9

⇒ 4 x = 9 +15

⇒ 4 x = 24

⇒ x = 6

### Thus, if (9/7)^{3 }× (49/81)^{(2x-6)} = (7/9)^{9 }then value of x is 6.

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