1. Simplify the quotient (6.4 x 10^9) / (1.6 x 10^-3). Write the answer in scientific notation.
My answer: 4 x 10^6?
Simplify.
2. a^16/a^4
My answer: a^12?
3. (4y^6/x^3)^2
My answer: 16^12/x^6?
4. (2/b^5)^-3
My answer: b^15/8?
#1 nope. If you subtract -3 from 9, you don't get 6.
4 x 10^12
#2 yes
#3 (4y^6/x^3)^2 = 16y^12/x^6
#4 yes
To simplify expressions involving exponents or scientific notation, you need to apply the rules of exponents and perform the necessary calculations.
Let's break down the steps for each question:
1. Simplify the quotient (6.4 x 10^9) / (1.6 x 10^-3):
To divide two numbers in scientific notation, divide their coefficients and subtract their exponents. In this case:
(6.4 x 10^9) / (1.6 x 10^-3) = (6.4 / 1.6) x (10^9 / 10^-3) = 4 x 10^(9 - (-3)) = 4 x 10^12
The correct answer is 4 x 10^12.
2. Simplify a^16/a^4:
When dividing variables with the same base, subtract their exponents. In this case:
a^16 / a^4 = a^(16 - 4) = a^12
So, the correct answer is a^12.
3. Simplify (4y^6/x^3)^2:
To raise an expression to a power, you multiply the exponents. In this case:
(4y^6/x^3)^2 = 4^2 x (y^6)^2 / (x^3)^2 = 16 x y^(6 * 2) / x^(3 * 2) = 16 x y^12 / x^6
Therefore, the correct answer is 16 x y^12 / x^6.
4. Simplify (2/b^5)^-3:
When raising a fraction to a negative exponent, you can flip the fraction and make the exponent positive. In this case:
(2/b^5)^-3 = (b^5/2)^3 = b^(5 * 3) / 2^3 = b^15 / 8
So, the correct answer is b^15 / 8.
Keep in mind that it's always good practice to double-check your calculations to ensure accuracy.