Solve for p 4^(2p)=4^(-2p-1)

$4^{2 p} = 4^{- 2 p - 1}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$4^{2 p} = 4^{- 2 p - 1}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 p = - 2 p - 1$

Step 3

Solve for $p$ .

Move all terms containing $p$ to the left side of the equation.

Add $2 p$ to both sides of the equation.

$2 p + 2 p = - 1$

Add $2 p$ and $2 p$ .

$4 p = - 1$

Divide each term in $4 p = - 1$ by $4$ and simplify.

Divide each term in $4 p = - 1$ by $4$ .

$\frac{4 p}{4} = \frac{- 1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 p}{4} = \frac{- 1}{4}$

Divide $p$ by $1$ .

$p = \frac{- 1}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$p = - \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{1}{4}$

Decimal Form:

$p = - 0.25$