In this work, we introduce a new unsupervised embedding method, Meta-Task Prompting with Explicit One-Word Limitation (MetaEOL), for generating high-quality sentence embeddings from Large Language Models (LLMs) without the need for model fine-tuning or task-specific engineering. Leveraging meta-task prompting, MetaEOL guides LLMs to produce embeddings through a series of carefully designed prompts that address multiple representational aspects. Our comprehensive experiments demonstrate that embeddings averaged from various meta-tasks yield competitive performance on Semantic Textual Similarity (STS) benchmarks and excel in downstream tasks, surpassing contrastive-trained models. Our findings suggest a new scaling law for embedding generation, offering a versatile, resource-efficient approach for embedding extraction across diverse sentence-centric scenarios.