What is (1/2 x^2)(2/5 x^5) ?

The solution to (1/2 x^2)(2/5 x^5) is (x^7)/5

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simplify (1/2 x^2)(2/5 x^5)

simplify

(\frac{1}{2} x^{2}) (\frac{2}{5} x^{5})

\frac{x ^{7}}{5}

Solution steps

(\frac{1}{2} x^{2}) (\frac{2}{5} x^{5})

Apply exponent rule:

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

x^{2} x^{5} = x^{2 + 5}

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

Add the numbers:

2 + 5 = 7

= \frac{1}{2} \cdot \frac{2}{5} x^{7}

Multiply fractions:

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

= \frac{1 \cdot 2 x ^{7}}{2 \cdot 5}

Cancel the common factor:

2

= \frac{1 \cdot x ^{7}}{5}

Multiply:

1 \cdot x^{7} = x^{7}

= \frac{x ^{7}}{5}

2 x - 5 = x - 3

6 (4 - x) = 2 x

x^{2} + 10 x + 22 = 31

6 x^{2} - 2 x + 36 = 5 x^{2} + 10 x

8 + \frac{1}{2}