What is (25(2)^t)*(150(1.5)^t) ?

The solution to (25(2)^t)*(150(1.5)^t) is 1250*3^{t+1}

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simplify (25(2)^t)*(150(1.5)^t)

simplify

(25 (2)^{t}) \cdot (150 (1.5)^{t})

1250 \cdot 3^{t + 1}

Solution steps

(25 (2)^{t}) (150 (1.5)^{t})

Apply exponent rule:

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

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

= 25 \cdot 150 (2 \cdot 1.5)^{t}

Multiply the numbers:

2 \cdot 1.5 = 3

= 25 \cdot 150 \cdot 3^{t}

Factor integer

150 = 3 \cdot 50

= 25 \cdot 3^{t} \cdot 3 \cdot 50

Apply exponent rule:

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

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

= 25 \cdot 3^{t + 1} \cdot 50

Multiply the numbers:

25 \cdot 50 = 1250

= 1250 \cdot 3^{t + 1}

2 a^{- \frac{3}{2}} e^{- \frac{r}{a}}

\frac{1 - x}{1 + x}

- 2 e^{- (1)^{2}} (1)

e^{2 t} (e^{2 t} + 1 - sin (2 t))

What is (25(2)^t)*(150(1.5)^t) ?
The solution to (25(2)^t)*(150(1.5)^t) is 1250*3^{t+1}