What is (12x^2y^4)(1/2 x^5y) ?

The solution to (12x^2y^4)(1/2 x^5y) is 6x^7y^5

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simplify (12x^2y^4)(1/2 x^5y)

simplify

(12 x^{2} y^{4}) (\frac{1}{2} x^{5} y)

6 x^{7} y^{5}

Solution steps

(12 x^{2} y^{4}) (\frac{1}{2} x^{5} y)

Apply exponent rule:

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

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

= 12 y^{4} \frac{1}{2} x^{2 + 5} y

Add the numbers:

2 + 5 = 7

= 12 y^{4} \frac{1}{2} x^{7} y

Apply exponent rule:

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

y^{4} y = y^{4 + 1}

= 12 \cdot \frac{1}{2} x^{7} y^{4 + 1}

Add the numbers:

4 + 1 = 5

= 12 \cdot \frac{1}{2} x^{7} y^{5}

Multiply fractions:

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

= \frac{1 \cdot 12 x ^{7} y ^{5}}{2}

Multiply the numbers:

1 \cdot 12 = 12

= \frac{12 x ^{7} y ^{5}}{2}

Divide the numbers:

\frac{12}{2} = 6

= 6 x^{7} y^{5}

4 (x - 4) = 14 - 6 (4 x + 1)

\frac{15 a - 3}{24}

x^{2} - x - 10 = 2

199 - 2 x^{2} = x^{2} + 33 x + 28

6 m^{3} + 8 m^{2} + 9 m + 12