# Quotient of powers Calculator

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Difficult Problems

1

Example

$\left(\frac{4}{3} x^2 y^3\right)^3\left(\frac{3}{16x^5}\right)^2$
2

Divide $4$ by $3$

$\left(\frac{3}{16x^5}\right)^2\left(\frac{4}{3}y^3x^2\right)^3$
3

The power of a product is equal to the product of it's factors raised to the same power

$\frac{64}{27}\left(\frac{3}{16x^5}\right)^2\left(y^3\right)^3x^{6}$
4

Applying the power of a power property

$\frac{64}{27}\left(\frac{3}{16x^5}\right)^2y^{9}x^{6}$
5

Taking out the constant $1$ from the fraction's denominator

$\frac{64}{27}\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{16}\cdot\frac{3}{x^5}}{16}}{16}}{16}}{16}}{16}}{16}}{16}}{16}}{16}}{16}}{16}\right)^2y^{9}x^{6}$
6

The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$\frac{64}{27}\cdot\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\left(\frac{1}{16}\cdot\frac{3}{x^5}\right)^2}{256}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}y^{9}x^{6}$

### Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "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": 0.8614423274993896, "perplexity": 912.4147422566826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "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-2018-47/segments/1542039745486.91/warc/CC-MAIN-20181119064334-20181119090334-00118.warc.gz"}