What is the answer to 81^{2p+3}*27= 1/27 ?

The answer to 81^{2p+3}*27= 1/27 is p=-9/4

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81^{2p+3}*27= 1/27

8 1^{2 p + 3} \cdot 27 = \frac{1}{27}

p = - \frac{9}{4}

Decimal Notation

p = - 2.25

Solution steps

8 1^{2 p + 3} \cdot 27 = \frac{1}{27}

Divide both sides by

27

8 1^{2 p + 3} = \frac{1}{729}

Apply exponent rules

2 (2 p + 3) = - 3

Solve

2 (2 p + 3) = - 3 : p = - \frac{9}{4}

p = - \frac{9}{4}

2^{2 x + 1} - 5 (2^{x}) + 2 = 0

2^{2 x - 2} - 2^{x + 1} = 2^{x} - 2^{3}

e^{3 - 2 x} = 4

2 (3^{2 x - 1}) = 4^{x + 1}

4^{3 x} = 32

What is the answer to 81^{2p+3}*27= 1/27 ?
The answer to 81^{2p+3}*27= 1/27 is p=-9/4
Solve for p: 81^{2p+3}*27= 1/27
The solution is p=-9/4