Simplify A^6 x a^2b^-2

44,909 in scientific notation

Simplify (a^2b^3)(a^5)

Simplify x^-5y^-6

What is the P(H,H,H,H,T,T,T,) on 7 flips of a coin?

on the last:

probability in that order= (1/2)^7

To simplify expressions involving exponents, we need to apply the properties of exponents. Let's go through each question step by step:

1. Simplify A^6 x a^2b^-2:
To multiply exponents with the same base, we add the exponents. Therefore, A^6 x a^2b^-2 can be simplified as A^6 x a^2/b^2.

2. Scientific notation of 44,909:
To write a number in scientific notation, we need to express it as a product of a decimal number between 1 and 10 and a power of 10.
44,909 in scientific notation can be written as 4.4909 x 10^4.

3. Simplify (a^2b^3)(a^5):
To multiply variables with the same base, we add the exponents. Therefore, (a^2b^3)(a^5) simplifies to a^(2+5) x b^(3+0), which further simplifies to a^7 x b^3.

4. Simplify x^-5y^-6:
To simplify negative exponents, we can rewrite them as reciprocals. Therefore, x^-5y^-6 can be expressed as 1/x^5 x 1/y^6 or (1/x^5)(1/y^6).

5. Probability of getting H,H,H,H,T,T,T in 7 flips of a coin:
The probability of getting heads (H) or tails (T) on a single flip of a fair coin is 1/2. Since each flip is independent of the others, we multiply the probabilities together.

The probability of getting H,H,H,H,T,T,T in 7 flips is (1/2)^4 x (1/2)^3 because there are 4 heads and 3 tails. Simplifying this expression, we get 1/16 x 1/8, which equals 1/128.

So, the probability of getting H,H,H,H,T,T,T in 7 flips of a coin is 1/128.