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 (302^t)(8*1.5^t)

simplify

(30 \cdot 2^{t}) \cdot (8 \cdot 1. 5^{t})

80 \cdot 3^{t + 1}

Solution steps

(30 \cdot 2^{t}) (8 \cdot 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 (2.8 \cdot 1 0^{- 6})

(9.32 \cdot 1 0^{3}) (3.32 \cdot 1 0^{2})

4.14 \cdot 1 0^{5} (20 \cdot 1 0^{- 6})

(3 x^{2} y^{3}) \cdot (\frac{5}{2} x^{2} y^{3})

20 e^{- 2 (0.5)}