Algebra
Topics

# How do you simplify  (-2x^2y)^3(5xy^3)^2?

Dec 1, 2017

$- 200 {x}^{8} {y}^{9}$

#### Explanation:

${\left(- 2 {x}^{2} y\right)}^{\textcolor{red}{3}} {\left(5 x {y}^{3}\right)}^{\textcolor{b l u e}{2}}$

First, use the exponent rule ${\left({x}^{a}\right)}^{b} = {x}^{a b}$

$\left({\left(- 2\right)}^{\textcolor{red}{3}} {x}^{2 \cdot \textcolor{red}{3}} {y}^{1 \cdot \textcolor{red}{3}}\right) \left({5}^{\textcolor{b l u e}{2}} {x}^{1 \cdot \textcolor{b l u e}{2}} {y}^{3 \cdot \textcolor{b l u e}{2}}\right)$

Simplify.

$\left(- 8 {x}^{6} {y}^{3}\right) \left(25 {x}^{2} {y}^{6}\right)$

Multiply the coefficients $- 8$ and $25$

$- 200 \left({x}^{\textcolor{red}{6}} {y}^{\textcolor{b l u e}{3}}\right) \left({x}^{\textcolor{red}{2}} {y}^{\textcolor{b l u e}{6}}\right)$

Next, use the exponent rule ${x}^{a} \cdot {x}^{b} = {x}^{a b}$

$- 200 {x}^{\left(\textcolor{red}{6 + 2}\right)} {y}^{\left(\textcolor{b l u e}{3 + 6}\right)}$

$- 200 {x}^{8} {y}^{9}$

##### Impact of this question
322 views around the world
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 11, "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, "math_score": 0.961940348148346, "perplexity": 6824.418879100117}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987795253.70/warc/CC-MAIN-20191021221245-20191022004745-00100.warc.gz"}