What is (2x^3)(1/4 x^2) ?

The solution to (2x^3)(1/4 x^2) is (x^5)/2

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simplify (2x^3)(1/4 x^2)

simplify

(2 x^{3}) (\frac{1}{4} x^{2})

\frac{x ^{5}}{2}

Solution steps

(2 x^{3}) (\frac{1}{4} x^{2})

Apply exponent rule:

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

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

= 2 \cdot \frac{1}{4} x^{3 + 2}

Add the numbers:

3 + 2 = 5

= 2 \cdot \frac{1}{4} x^{5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2 x ^{5}}{4}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2 x ^{5}}{4}

Cancel the common factor:

2

= \frac{x ^{5}}{2}

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

(d x + e^{3 x} d y) (e^{- 3 x})

a + 1 a^{2} - 1

π

2 e^{- 1.25 π}