What is 15d^{15}e^{15}f^2*5d^5e^5f ?

The solution to 15d^{15}e^{15}f^2*5d^5e^5f is 75e^{20}d^{20}f^3

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simplify 15d^{15}e^{15}f^2*5d^5e^5f

simplify

15 d^{15} e^{15} f^{2} \cdot 5 d^{5} e^{5} f

75 e^{20} d^{20} f^{3}

Solution steps

15 d^{15} e^{15} f^{2} \cdot 5 d^{5} e^{5} f

Apply exponent rule:

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

e^{15} e^{5} = e^{15 + 5}

= 15 d^{15} f^{2} \cdot 5 d^{5} e^{15 + 5} f

Add the numbers:

15 + 5 = 20

= 15 d^{15} f^{2} \cdot 5 d^{5} e^{20} f

Apply exponent rule:

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

d^{15} d^{5} = d^{15 + 5}

= 15 f^{2} \cdot 5 d^{15 + 5} e^{20} f

Add the numbers:

15 + 5 = 20

= 15 f^{2} \cdot 5 d^{20} e^{20} f

Apply exponent rule:

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

f^{2} f = f^{2 + 1}

= 15 \cdot 5 d^{20} e^{20} f^{2 + 1}

Add the numbers:

2 + 1 = 3

= 15 \cdot 5 d^{20} e^{20} f^{3}

Multiply the numbers:

15 \cdot 5 = 75

= 75 e^{20} d^{20} f^{3}

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What is 15d^{15}e^{15}f^2*5d^5e^5f ?
The solution to 15d^{15}e^{15}f^2*5d^5e^5f is 75e^{20}d^{20}f^3