What is (3x^2y^6z)(15xyz) ?

The solution to (3x^2y^6z)(15xyz) is 45x^3y^7z^2

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simplify (3x^2y^6z)(15xyz)

simplify

(3 x^{2} y^{6} z) (15 x yz)

45 x^{3} y^{7} z^{2}

Solution steps

(3 x^{2} y^{6} z) (15 x yz)

Apply exponent rule:

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

x^{2} x = x^{2 + 1}

= 3 y^{6} z \cdot 15 x^{2 + 1} yz

Add the numbers:

2 + 1 = 3

= 3 y^{6} z \cdot 15 x^{3} yz

Apply exponent rule:

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

y^{6} y = y^{6 + 1}

= 3 z \cdot 15 x^{3} y^{6 + 1} z

Add the numbers:

6 + 1 = 7

= 3 z \cdot 15 x^{3} y^{7} z

Apply exponent rule:

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

zz = z^{1 + 1}

= 3 \cdot 15 x^{3} y^{7} z^{1 + 1}

Add the numbers:

1 + 1 = 2

= 3 \cdot 15 x^{3} y^{7} z^{2}

Multiply the numbers:

3 \cdot 15 = 45

= 45 x^{3} y^{7} z^{2}

3 e^{x} \cdot e^{- x}

a^{(a + b)} \cdot b^{(a + b)}

(6.51 x 1 0^{- 11}) (7.8 x 1 0^{- 18})

\frac{e ^{- 4 x}}{e ^{x}}