Find each product or Quotient. Express using exponents.

1. The quotient of a to the 8th power and a to the 8th power? a
2. The quotient of -x to the 5th power and -x? -x to the 4th power
3. (15/5)(n to the 9th power/ n)? 3n go the 10th power

Neutral water has a pH of 7. Each one-unit decrease i the pH means that the solution is 10 times more acidic. How much more acidic vinegar is than baking soda if vinegar has a ph of 3 and baking soda has a ph of 9? I think the answer is 10 to the 6th power but I don't know how to write out my work.

if this is what you mean

1) a^8/a^8 = 1

2) -x^5/-x^4 = x

3) 15/5 * n^9/n = 3n^8

Also, use separate posts for 2 different questions/subjects

yes and sorry all the questions I asked are on the same homework paper

vinegar - pH 3

baking soda - pH 9
9 - 3 = 6 units diff.
10 x 6 = 60x as acidic

10^6 = 1 million, so I can't see how that is right

10^1.77815 = 60

I am not a tutor, so you might want to repost this as a separate question

Okay thank you

:) that's ok. also, you will have better response if posted separate.

raise 8 to the 5th power, then find the quotient of the result and j

To find each product or quotient and express using exponents, you need to follow the rules of exponentiation.

1. The quotient of a to the 8th power and a to the 8th power: When dividing two numbers with the same base, you subtract the exponents. In this case, a raised to the 8th power divided by a raised to the 8th power would yield a result of a raised to the (8 - 8) power, which is a^0. Any number (except zero) raised to the power of zero is equal to 1. So, the answer is 1.

2. The quotient of -x to the 5th power and -x: Similar to the previous question, when dividing two numbers with the same base, you subtract the exponents. In this case, (-x) raised to the 5th power divided by (-x) would yield (-x) raised to the (5 - 1) power, which is (-x)^4.

3. (15/5)(n to the 9th power / n): To find the product of two terms with exponents, you simply multiply the coefficients and add the exponents of the same variable. In this case, (15/5) is equal to 3, and n raised to the 9th power divided by n would yield n raised to the (9 - 1) power. So, the expression simplifies to 3n^8.

Regarding your question about the acidity of vinegar compared to baking soda, let's calculate the difference:

The pH scale is a logarithmic scale, which means that for every one-unit difference in pH, the concentration changes by a factor of 10.
Given that vinegar has a pH of 3 and baking soda has a pH of 9, the difference in pH is 9 - 3 = 6.

Since each one-unit decrease in pH means the solution is 10 times more acidic, a six-unit difference indicates that vinegar is 10^6 (10 to the 6th power) times more acidic than baking soda.

So, you are correct, the answer is 10^6.