Solve the equation. Put only integers or decimals for your answer.

Question

Solve the equation. Put only integers or decimals for your answer. $$ 16^{-3}=4^{2 x} $$

UpStudy AI · Accepted Answer

The equation to solve is:

$$
16^{-3} = 4^{2x}
$$

First, express both sides with the same base. Notice that $$16$$ is a power of $$4$$:

$$
16 = 4^2
$$

Substitute $$16$$ with $$4^2$$ in the equation:

$$
(4^2)^{-3} = 4^{2x}
$$

Simplify the left side using the power of a power property $$(a^m)^n = a^{m \times n}$$:

$$
4^{-6} = 4^{2x}
$$

Since the bases are the same, set the exponents equal to each other:

$$
-6 = 2x
$$

Solve for $$x$$:

$$
x = \frac{-6}{2} = -3
$$

**Answer:**  
-3
$$ x = -3 $$

Upstudy AI Solution