$$ 1 \leftarrow \quad $$ If $$ 15^{-x}=8 $$, what does $$ 15^{2 x} $$ equal?

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UpStudy AI · Accepted Answer

1. Given the equation $$15^{-x} = 8$$, we start by rewriting the left-hand side using the property of exponents:
   $$
   15^{-x} = \frac{1}{15^x}
   $$
   
2. Therefore, we have:
   $$
   \frac{1}{15^x} = 8
   $$
   Taking the reciprocal on both sides gives:
   $$
   15^x = \frac{1}{8}
   $$

3. To find $$15^{2x}$$, we use the property of exponents:
   $$
   15^{2x} = \left(15^x\right)^2
   $$
   
4. Substituting the value of $$15^x$$ we obtained:
   $$
   15^{2x} = \left(\frac{1}{8}\right)^2 = \frac{1}{64}
   $$

Thus, the final answer is:
$$
15^{2x} = \frac{1}{64}
$$
$$15^{2x} = \frac{1}{64}$$

If , what does equal?

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