Question 173954
Simplify:
1. {{{((14z^3)/(15y^3))*(10z^2/4y)}}} Multiply the numerators and the denominators.
{{{(140z^5)/(60y^4)}}} Reduce the numerical part of the fraction.
{{{highlight(7z^5/3y^4)}}}
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2. {{{((7v^4w^5)/(16u))*((5v^2)/(8u^4v^6))}}} Multiply the numerators and the denominators.
{{{(35cross(v^6)w^5)/(128u^5cross(v^6))}}} Cancel the indicated factors.
{{{highlight((35w^5)/(128u^5))}}}
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3. {{{((u^2+16u+63)/(u+7))*(1/(u+9))}}} Multiply the numerators and the denominators.
{{{(u^2+16u+63)/((u+7)(u+9))}}} Multiply the factors in the denominator.
{{{cross(u^2+16u+63)/cross(u^2+16u+63)}}}={{{highlight(1)}}}
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4. {{{((24x^3z^2)/(6y^2))/((8xz^4)/(3y^4))}}} Invert the lower fraction and multiply.
{{{((24x^3z^2)/(6y^2))*((3y^4)/(8xz^4))}}} Multiply the numerators and the denominators.
{{{(72x^3y^4z^2)/(48xy^2z^4)}}} Reduce the numerical part of the fraction.
{{{(3x^3y^4z^2)/(2xy^2z^4)}}} Factor the variables.
{{{(3*cross(x)*x^2*cross(y^2)*y^2*cross(z^2))/(2*cross(x)*cross(y^2)*z^2*cross(z^2))}}} Cancel the indicated factors.
{{{highlight((3x^2y^2)/(2z^2))}}}
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5. {{{((z^2-10z+21)/(z^2-13z+36))/((z^2-11z+24)/(z^2-9z+14))}}} Invert the lower fraction and multiply.
{{{((z^2-10z+21)/(z^2-13z+36))*((z^2-9z+14)/(z^2-11z+24))}}} Before multiplying, factor the numerators and the denominators.
{{{((cross(z-3)(z-7))/((z-4)(z-9)))*(((z-2)(z-7))/(cross(z-3)(z-8)))}}} Cancel the indicated factors.
{{{((z-7)/((z-4)(z-9)))*(((z-2)(z-7))/(z-8)))}}}
{{{((z-7)(z-2)(z-7))/((z-4)(z-9)(z-8))}}} Multiply the numerators and the denominators.
{{{highlight((z^3-16z^2+77z-98)/(z^3-21z^2+140z-288))}}}