How do you simplify $\frac{\frac{20 t^{3} u}{7 r s^{3}}}{\frac{5 t^{5} u^{4}}{14 s^{4}}}$ $\frac { \frac { 20t ^ { 3} u } { 7r s ^ { 3} } } { \frac { 5t ^ { 5} u ^ { 4} } { 14s ^ { 4} } }$ ?

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How do you simplify $\frac{\frac{20 t^{3} u}{7 r s^{3}}}{\frac{5 t^{5} u^{4}}{14 s^{4}}}$ $\frac { \frac { 20t ^ { 3} u } { 7r s ^ { 3} } } { \frac { 5t ^ { 5} u ^ { 4} } { 14s ^ { 4} } }$ ?

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Answer 1 · 2018-01-31T22:28:24

$\frac{280 s}{35 r t^{2} u^{3}}$ $(280s)/(35rt^2u^3)$

Explanation:

Key point here is Dividing by a fraction is the same thing as multiplying by its reciprocal.

$\frac{\frac{a}{b}}{\frac{c}{d}} = (\frac{a}{b}) \cdot (\frac{d}{c})$ $(a/b)/(c/d)= (a/b)*(d/c)$

So

$\frac{\frac{20 t^{3} u}{7 r s^{3}}}{\frac{5 t^{5} u^{4}}{14 s^{4}}} = \frac{20 t^{3} u}{7 r s^{3}} \cdot \frac{14 s^{4}}{5 t^{5} u^{4}}$ $((20t^3u)/(7rs^3))/((5t^5u^4)/(14s^4))=(20t^3u)/(7rs^3)*(14s^4)/(5t^5u^4)$

From here, since we are multiplying fractions we can simply put everything together. (AKA combine like terms)

$\frac{(20 \cdot 14) s^{4} t^{3} u}{(7 \cdot 5) r s^{3} t^{5} u^{4}}$ $((20*14)s^4t^3u)/((7*5)rs^3t^5u^4)$

Now looking at exponents we know that $s^{4} = s^{3} \cdot s$ $s^4 = s^3 *s$

$\frac{(20 \cdot 14) s^{3} \cdot s t^{3} u}{(7 \cdot 5) r s^{3} t^{5} u^{4}}$ $((20*14)color(red)(s^3 * s)t^3u)/((7*5)rcolor(red)(s^3)t^5u^4)$

The $s^{3}$ $s^3$ cancels out and we use this same process for $t$ $t$ and $u$ $u$ .

Final answer would be

$\frac{280 s}{35 r t^{2} u^{3}}$ $(280s)/(35rt^2u^3)$

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How do you simplify $\frac{\frac{20 t^{3} u}{7 r s^{3}}}{\frac{5 t^{5} u^{4}}{14 s^{4}}}$ $\frac { \frac { 20t ^ { 3} u } { 7r s ^ { 3} } } { \frac { 5t ^ { 5} u ^ { 4} } { 14s ^ { 4} } }$ ?

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How do you simplify 20t3u7rs35t5u414s4\frac { \frac { 20t ^ { 3} u } { 7r s ^ { 3} } } { \frac { 5t ^ { 5} u ^ { 4} } { 14s ^ { 4} } }?

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How do you simplify $\frac{\frac{20 t^{3} u}{7 r s^{3}}}{\frac{5 t^{5} u^{4}}{14 s^{4}}}$ $\frac { \frac { 20t ^ { 3} u } { 7r s ^ { 3} } } { \frac { 5t ^ { 5} u ^ { 4} } { 14s ^ { 4} } }$ ?