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Popular >

simplify 2e^{3t}*6^{3t}

Solution

simplify

2 e^{3 t} \cdot 6^{3 t}

Solution

2 7^{t} \cdot 2^{3 t + 1} e^{3 t}

Solution steps

2 e^{3 t} \cdot 6^{3 t}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

6^{3 t} e^{3 t} = (6 e)^{3 t}

= 2 (6 e)^{3 t}

(e 6)^{3 t} = 6^{3 t} e^{3 t}

= 2 \cdot 6^{3 t} e^{3 t}

Factor integer

6 = 2 \cdot 3

= 2 e^{3 t} (2 \cdot 3)^{3 t}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 3)^{3 t} = 2^{3 t} \cdot 3^{3 t}

= 2 e^{3 t} \cdot 2^{3 t} \cdot 3^{3 t}

Apply exponent rule:

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

2 \cdot 2^{3 t} = 2^{1 + 3 t}

= e^{3 t} \cdot 2^{1 + 3 t} \cdot 3^{3 t}

3^{3 t} = 2 7^{t}

= 2 7^{t} \cdot 2^{3 t + 1} e^{3 t}

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Frequently Asked Questions (FAQ)

What is 2e^{3t}*6^{3t} ?
The solution to 2e^{3t}*6^{3t} is 27^t*2^{3t+1}e^{3t}