What is (3x^2)^{2x}(x^2+2x)^2 ?

The solution to (3x^2)^{2x}(x^2+2x)^2 is 9^xx^{4x}(x^2+2x)^2

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simplify (3x^2)^{2x}(x^2+2x)^2

simplify

(3 x^{2})^{2 x} (x^{2} + 2 x)^{2}

9^{x} x^{4 x} (x^{2} + 2 x)^{2}

Solution steps

(3 x^{2})^{2 x} (x^{2} + 2 x)^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 x^{2})^{2 x} = 3^{2 x} (x^{2})^{2 x}

= 3^{2 x} (x^{2})^{2 x} (x^{2} + 2 x)^{2}

Simplify

(x^{2})^{2 x} : x^{4 x}

= 3^{2 x} x^{4 x} (x^{2} + 2 x)^{2}

3^{2 x} = 9^{x}

= 9^{x} x^{4 x} (x^{2} + 2 x)^{2}

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\int_{0}^{3} x^{2} + 9 d x

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\int x^{2} - x - 6 d x

What is (3x^2)^{2x}(x^2+2x)^2 ?
The solution to (3x^2)^{2x}(x^2+2x)^2 is 9^xx^{4x}(x^2+2x)^2