Determine the integer value of n that satisfies the the equation. 4^n=16 3^n=1/81
1 answer:
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Answer:
8 different combinations are possible.
Step-by-step explanation:
Here, we have 2 different combinations for each time.
And the player comes out to bat 3 times.
So, total number of combinations are:
i.e. a total of 8 number of times.
Let a hit is termed as 'H' and an out is termed as 'O'.
Total combinations are:
{HHH, HHO, HOH, HOO, OHH, OHO, OOH, OOO}
Kindly have a look at the tree diagram attached in the answer area.
In starting, there are 2 combinations possible, i.e. 'O' and 'H'.
After 'O' , 2 possible i.e. 'O' and 'H'.
After 'H' , 2 possible i.e. 'O' and 'H'.
and so on....
(9)^4 × (27)^3 × (81)^2 / (3)^24 = 3.
Explanation:
- All the numbers in the numerator i.e. 9, 27, 81 are multiples of 3.
- 9 = 3 × 3 = 3², 27 = 3 × 3 × 3 = 3³, 81 = 3 × 3 × 3 × 3 =
.
= (3^2)^4, 27³ = (3^3)^3, 81^2 = (3^4)^2.
- According to the power rule, (a^x)^y = a^xy.
- So the given numbers can be written as follows
- According to the product rule, (a^x) × (a^y) = a^xy.
- So the numerator can be written as
- So the fraction becomes 3^25 / 3^24 = 3 × 3^24 / 3^24 = 3.