What is 1/5 (de^3)(5d^3e)(-8d^6e^7) ?

The solution to 1/5 (de^3)(5d^3e)(-8d^6e^7) is -8e^{11}d^{10}

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simplify 1/5 (de^3)(5d^3e)(-8d^6e^7)

simplify

\frac{1}{5} (d e^{3}) (5 d^{3} e) (- 8 d^{6} e^{7})

- 8 e^{11} d^{10}

Solution steps

\frac{1}{5} (d e^{3}) (5 d^{3} e) (- 8 d^{6} e^{7})

Apply exponent rule:

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

e^{3} e = e^{3 + 1}

= \frac{1}{5} d \cdot 5 d^{3} e^{3 + 1} (- 8 d^{6} e^{7})

Add the numbers:

3 + 1 = 4

= \frac{1}{5} d \cdot 5 d^{3} e^{4} (- 8 d^{6} e^{7})

Apply exponent rule:

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

d d^{3} = d^{1 + 3}

= \frac{1}{5} \cdot 5 d^{1 + 3} e^{4} (- 8 d^{6} e^{7})

Add the numbers:

1 + 3 = 4

= \frac{1}{5} \cdot 5 d^{4} e^{4} (- 8 d^{6} e^{7})

Remove parentheses:

(- a) = - a

= - \frac{1}{5} \cdot 5 d^{4} e^{4} \cdot 8 d^{6} e^{7}

Multiply fractions:

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

= - \frac{1 \cdot 5 d ^{4} e ^{4} \cdot 8 d ^{6} e ^{7}}{5}

Cancel the common factor:

5

= - 1 \cdot d^{4} e^{4} \cdot 8 d^{6} e^{7}

Multiply the numbers:

1 \cdot 8 = 8

= - 8 e^{7} e^{4} d^{6} d^{4}

Apply exponent rule:

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

e^{4} e^{7} = e^{4 + 7}

= - 8 d^{4} d^{6} e^{4 + 7}

Add the numbers:

4 + 7 = 11

= - 8 d^{4} d^{6} e^{11}

Apply exponent rule:

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

d^{4} d^{6} = d^{4 + 6}

= - 8 d^{4 + 6} e^{11}

Add the numbers:

4 + 6 = 10

= - 8 d^{10} e^{11}

((\frac{- 5}{6})^{3})^{5}^{7}

x^{2} \circ x^{3}

\frac{β}{α} x^{β - 1} e^{- \frac{x ^{β}}{α}}

1.67 \cdot 1 0^{- 27} \cdot (3 \cdot 1 0^{8})^{2}

(7 x^{3}) \cdot (3 x^{2} y)

What is 1/5 (de^3)(5d^3e)(-8d^6e^7) ?
The solution to 1/5 (de^3)(5d^3e)(-8d^6e^7) is -8e^{11}d^{10}