What is (30(2)^t)*(8(1.5)^t) ?

The solution to (30(2)^t)*(8(1.5)^t) is 80*3^{t+1}

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simplify (30(2)^t)*(8(1.5)^t)

simplify

(30 (2)^{t}) \cdot (8 (1.5)^{t})

80 \cdot 3^{t + 1}

Solution steps

(30 (2)^{t}) (8 (1.5)^{t})

Apply exponent rule:

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

2^{t} \cdot 1. 5^{t} = (2 \cdot 1.5)^{t}

= 30 \cdot 8 (2 \cdot 1.5)^{t}

Multiply the numbers:

2 \cdot 1.5 = 3

= 30 \cdot 8 \cdot 3^{t}

Factor integer

30 = 3 \cdot 10

= 3 \cdot 10 \cdot 3^{t} \cdot 8

Apply exponent rule:

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

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

= 10 \cdot 3^{1 + t} \cdot 8

Multiply the numbers:

10 \cdot 8 = 80

= 80 \cdot 3^{t + 1}

2.6 \cdot 1 0^{- 4}

4.8456 e^{- 0.2019}

(e^{\frac{- x}{2}})^{2}

x^{2} (x - 4)^{2}

t^{2} e^{- 2 t} sin (2 t)

What is (30(2)^t)*(8(1.5)^t) ?
The solution to (30(2)^t)*(8(1.5)^t) is 80*3^{t+1}