How do evaluate $\frac{15 x^{14} y^{14}}{3 x^{6} y^{2}}$ $\frac { 15x ^ { 14} y ^ { 14} } { 3x ^ { 6} y ^ { 2} }$ ?

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Answer 1 · 2018-03-05T02:23:19

See a solution process below:

First, rewrite the expression as:

$(\frac{15}{3}) (\frac{x^{14}}{x^{6}}) (\frac{y^{14}}{y^{2}}) \Rightarrow$ $(15/3)(x^14/x^6)(y^14/y^2) =>$

$5 (\frac{x^{14}}{x^{6}}) (\frac{y^{14}}{y^{2}})$ $5(x^14/x^6)(y^14/y^2)$

Now, use this rule of exponents to complete the simplification:

$\frac{x^{a}}{x^{b}} = x^{a - b}$ $x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))$

$5 (\frac{x^{14}}{x^{6}}) (\frac{y^{14}}{y^{2}}) \Rightarrow$ $5(x^color(red)(14)/x^color(blue)(6))(y^color(red)(14)/y^color(blue)(2)) =>$

$5 x^{14 - 6} y^{14 - 2} \Rightarrow$ $5x^(color(red)(14)-color(blue)(6))y^(color(red)(14)-color(blue)(2)) =>$

$5 x^{8} y^{12}$ $5x^8y^12$

How do evaluate \frac { 15x ^ { 14} y ^ { 14} } { 3x ^ { 6} y ^ { 2} }15x14y143x6y2\frac { 15x ^ { 14} y ^ { 14} } { 3x ^ { 6} y ^ { 2} }?