What is (y^{3x^2+8/2 x-1/3})/(y^{x^2+7/2 x-1/4)} ?

The solution to (y^{3x^2+8/2 x-1/3})/(y^{x^2+7/2 x-1/4)} is y^{(24x^2-1+6x)/(12)}

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simplify (y^{3x^2+8/2 x-1/3})/(y^{x^2+7/2 x-1/4)}

simplify

\frac{y ^{3 x^{2} + \frac{8}{2} x - \frac{1}{3}}}{y ^{x^{2} + \frac{7}{2} x - \frac{1}{4}}}

y^{\frac{24 x ^{2} - 1 + 6 x}{12}}

Solution steps

\frac{y ^{3 x^{2} + \frac{8}{2} x - \frac{1}{3}}}{y ^{x^{2} + \frac{7}{2} x - \frac{1}{4}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

= y^{3 x^{2} + \frac{8}{2} x - \frac{1}{3} - x^{2} - \frac{7}{2} x - (- \frac{1}{4})}

Simplify

y^{3 x^{2} + \frac{8}{2} x - \frac{1}{3} - x^{2} - \frac{7}{2} x - (- \frac{1}{4})} : y^{- \frac{1}{12} + \frac{x}{2} + 2 x^{2}}

= y^{- \frac{1}{12} + \frac{x}{2} + 2 x^{2}}

Simplify

- \frac{1}{12} + \frac{x}{2} + 2 x^{2} : \frac{24 x ^{2} - 1 + 6 x}{12}

= y^{\frac{24 x ^{2} - 1 + 6 x}{12}}

4 x - 5 = 3 x - 2

5 x - 4 < 8 + 9 x

4 - 3 ∣ 5 x + 10 ∣ \leq - 10

- 45 = - 5 x - 10

\frac{( 2 h ^{2} k ) ^{4}}{( 7 h ^{- 1} k ^{2} ) ^{2}}

What is (y^{3x^2+8/2 x-1/3})/(y^{x^2+7/2 x-1/4)} ?
The solution to (y^{3x^2+8/2 x-1/3})/(y^{x^2+7/2 x-1/4)} is y^{(24x^2-1+6x)/(12)}