What is (5*10^a)*(9*10^b) ?

The solution to (5*10^a)*(9*10^b) is 9*5^{a+b+1}*2^{a+b}

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simplify (510^a)(9*10^b)

simplify

(5 \cdot 1 0^{a}) \cdot (9 \cdot 1 0^{b})

9 \cdot 5^{a + b + 1} \cdot 2^{a + b}

Solution steps

(5 \cdot 1 0^{a}) (9 \cdot 1 0^{b})

Apply exponent rule:

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

1 0^{a} \cdot 1 0^{b} = 1 0^{a + b}

= 5 \cdot 9 \cdot 1 0^{a + b}

Factor integer

10 = 5 \cdot 2

= 5 \cdot 9 (5 \cdot 2)^{a + b}

Apply exponent rule:

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

(5 \cdot 2)^{a + b} = 5^{a + b} \cdot 2^{a + b}

= 5 \cdot 9 \cdot 5^{a + b} \cdot 2^{a + b}

Apply exponent rule:

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

5 \cdot 5^{a + b} = 5^{1 + a + b}

= 9 \cdot 5^{1 + a + b} \cdot 2^{a + b}

e^{- x} (- x e^{- a x})

10000 \cdot (1 + 0.0180875824 \cdot 12)^{- 1}

3 (5 - 2 x)^{- 1}

(5 mn) (7 m^{3} p^{2}) (4 n^{5} p)

What is (5*10^a)*(9*10^b) ?
The solution to (5*10^a)*(9*10^b) is 9*5^{a+b+1}*2^{a+b}