# How do you simplify (216r^9)^(1/3)?

$6 {r}^{3}$
${\left(216 {r}^{9}\right)}^{\frac{1}{3}} = {\left({6}^{3} \cdot {r}^{9}\right)}^{\frac{1}{3}}$
Recall that ${\left({a}^{m}\right)}^{n} = {a}^{m \times n}$
Thus ${\left({6}^{3} \cdot {r}^{9}\right)}^{\frac{1}{3}} = {6}^{\frac{3}{3}} \cdot {r}^{\frac{9}{3}} = 6 {r}^{3}$
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://socratic.org/questions/how-do-you-simplify-216r-9-1-3", "fetch_time": 1721936958000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2024-30/segments/1720763861452.88/warc/CC-MAIN-20240725175545-20240725205545-00301.warc.gz", "warc_record_offset": 462365559, "warc_record_length": 5754, "token_count": 165, "char_count": 320, "score": 4.09375, "int_score": 4, "crawl": "CC-MAIN-2024-30", "snapshot_type": "latest", "language": "en", "language_score": 0.5040703415870667, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00039-of-00064.parquet"}