What is (10(x+y)^3)/(4(x+y)^{-2)} ?

The solution to (10(x+y)^3)/(4(x+y)^{-2)} is (5(x+y)^5)/2

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simplify (10(x+y)^3)/(4(x+y)^{-2)}

simplify

\frac{10 ( x + y ) ^{3}}{4 ( x + y ) ^{- 2}}

\frac{5 ( x + y ) ^{5}}{2}

Solution steps

\frac{10 ( x + y ) ^{3}}{4 ( x + y ) ^{- 2}}

Factor the number:

10 = 2 \cdot 5

= \frac{2 \cdot 5 ( x + y ) ^{3}}{4 ( x + y ) ^{- 2}}

Factor the number:

4 = 2 \cdot 2

= \frac{2 \cdot 5 ( x + y ) ^{3}}{2 \cdot 2 ( x + y ) ^{- 2}}

Cancel the common factor:

2

= \frac{5 ( x + y ) ^{3}}{2 ( x + y ) ^{- 2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x + y)^{3} = (x + y)^{- 2} (x + y)^{5}

= \frac{5 ( x + y ) ^{- 2} ( x + y ) ^{5}}{2 ( x + y ) ^{- 2}}

Cancel the common factor:

(x + y)^{- 2}

= \frac{5 ( x + y ) ^{5}}{2}

(7 y)^{2}

x^{\frac{3}{7}} \cdot x^{\frac{3}{14}}

- 3 + \frac{p}{7} = - 5

t^{2} - 2 t - 3

What is (10(x+y)^3)/(4(x+y)^{-2)} ?
The solution to (10(x+y)^3)/(4(x+y)^{-2)} is (5(x+y)^5)/2