How do you simplify #((5n^4)/(p^3))/((6n)/(5p))#?

Question

Eva Adamson · Accepted Answer

See the entire simplification process below:

First, simplify the division by using the rule for dividing fractions: #(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))# #(color(red)(5n^4)/color(blue)(p^3))/(color(green)(6n)/color(purple)(5p)) = (color(red)(5n^4) xx color(purple)(5p))/(color(blue)(p^3) xx color(green)(6n)) = (25n^4p)/(6np^3)# We can now use these rules for exponents to further simplify this expression: #x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))# #x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))# #a = a^color(red)(1)# #(25n^color(red)(4)p^color(red)(1))/(6n^color(blue)(1)p^color(blue)(3))# #(25n^(color(red)(4)-color(blue)(1)))/(6p^(color(blue)(3)-color(red)(1)))# #(25n^3)/(6p^2)#

Eli Assouline · Answer

undefined To simplify ((5n^4)/(p^3))/((6n)/(5p)), you can multiply the numerator and denominator of the first fraction by the reciprocal of the second fraction. This gives you (5n^4 * 5p) / (p^3 * 6n). Simplifying further, you get (25n^4p) / (6n * p^3). Now, cancel out the common factors between the numerator and denominator, which are n and p. This leaves you with 25n^3 / 6p^2 as the simplified form of the expression.

Savannah Anderson · Answer

undefined To simplify the expression $\frac{\frac{5n^4}{p^3}}{\frac{6n}{5p}}$, we can simplify the numerator and denominator separately before dividing:

For the numerator:
$\frac{5n^4}{p^3}$

For the denominator:
$\frac{6n}{5p}$

Now, let's simplify each part:

Numerator:
$\frac{5n^4}{p^3}$

Denominator:
$\frac{6n}{5p}$

Now, let's divide the numerator by the denominator:

$\frac{\frac{5n^4}{p^3}}{\frac{6n}{5p}} = \frac{5n^4}{p^3} \times \frac{5p}{6n}$

Simplify the expression by canceling out common factors:

$\frac{5n^4 \times 5p}{p^3 \times 6n} = \frac{25n^4p}{6p^3}$

Finally, we simplify further by canceling out $p$ from the numerator and denominator:

$\frac{25n^4}{6p^2}$