Question

Simplify the given expression. Assume that no variable equals 0. (14x20y10 / 28x12y14)4

Answer 1

Answer:

$\frac{1}{2^{4}*14^{3} *x^{28}*y^{46}}$

Step-by-step explanation:

To simplify the expression $\frac{14x^{20}y^{10}}{(2*14*x^{12} y^{14} )^{4}}$ first we need to raise every member of the denominator to the given exponent, number 4

Remember that $(x^{b} )^{c} =z^{b*c}$ where 'a' and 'b are natural numbers (any numbers you want

$\frac{14x^{20}*y^{10}}{2^{4}*14^{4}*x^{48}*y^{56}}$

Where we can make some operations, remember that $\frac{x^{a} }{x^{c} }=x^{a-c}$

$\frac{1}{2^{4}*14^{3} *x^{28}*y^{46}}$

We have assumed that nor x, nor y equals 0 in any moment, since if that would happen, we ca not simplify anything bacause error math 0/0.

Answer 2

Answer:

$\frac{1}{43904x^{28}y^{46}}$

Step-by-step explanation:

Simplify:

$\frac{14x^{20}y^{10}}{(28x^{12}y^{14})^4}$

Use this property in the denominator:

$(x^y)^z=x^{yz}$

And multiply each exponent in the denominator by 4:

$\frac{14x^{20}y^{10}}{(28^4x^{48}y^{56})}$

Use these properties:

$x^{-n}=\frac{1}{x^n}$

$x^yx^z=x^{y+z}$

And combine powers:

$\frac{14x^{20-48}y^{10-56}}{28^4} =\frac{14x^{-28} y^{-46}}{28^4} =\frac{14}{28^4 x^{28} y^{46}}$

Divide the constants:

$\frac{14}{28^4} =\frac{14}{614656} =\frac{1}{43904}$

Therefore, the simplied expression is:

$\frac{1}{43904x^{28}y^{46}}$