^ = exponent

**show work please

A sheet of 67-pound paper has a thickness of 100^-1 inch.

a. write and evaluate an expression for the total thickness of 5 sheets of 67-pound paper

b. write and evaluate an expression for the total thickness of 2^3 sheets of 67-pound paper.

I've been looking at this problem for a half hour now and i cannot figure it out... please help!!!

a.

5*(1/100) = 0.05

b.
2^3 = 8
.08

a.) 5*(1/100)= 5/100= .05

b.) 2^3=8 8*(1/100)= .08

Sure! Let's break it down step-by-step:

a. The thickness of one sheet of 67-pound paper is given as 100^-1 inch. To find the total thickness of 5 sheets, we need to multiply the thickness of one sheet by 5.

Expression for total thickness of 5 sheets: 5 * (100^-1)

To evaluate this expression, we simplify it step by step:

Step 1: 100^-1 = 1/100 (taking the reciprocal of 100)
Step 2: 5 * (1/100) = 5/100
Step 3: 5/100 = 1/20 (simplifying the fraction)

So, the total thickness of 5 sheets of 67-pound paper is 1/20 inch.

b. The expression for the total thickness of 2^3 sheets of 67-pound paper would be 2^3 * (100^-1).

To evaluate this expression, we simplify it step by step:

Step 1: 100^-1 = 1/100
Step 2: 2^3 = 2 * 2 * 2 = 8
Step 3: 8 * (1/100) = 8/100
Step 4: 8/100 = 2/25 (simplifying the fraction)

So, the total thickness of 2^3 sheets (8 sheets) of 67-pound paper is 2/25 inch.

Sure, I can help you with that!

Before we start, let's clarify the given information:
- A sheet of 67-pound paper has a thickness of 100^-1 inch.
- "^" represents an exponent.
- "**show work please" means that you need to explain step-by-step how to arrive at the answer.

Now let's work on the problem step by step:

a. To find the total thickness of 5 sheets of 67-pound paper, we need to multiply the thickness of one sheet by the number of sheets.

Given that the thickness of one sheet is 100^-1 inch (which is equivalent to 1/100 inch), we can write the expression for the total thickness of 5 sheets as: 5 * (1/100).

To evaluate this expression, we multiply 5 by 1/100: 5 * (1/100) = 5/100 = 0.05 inch.

So, the total thickness of 5 sheets of 67-pound paper is 0.05 inch.

b. Now let's consider the total thickness of 2^3 sheets of 67-pound paper. The exponent of 3 means that we need to multiply 2 by itself three times (2 * 2 * 2).

Given that the thickness of one sheet is 100^-1 inch (which is 1/100 inch), we can write the expression for the total thickness of 2^3 sheets as: (1/100) * 2 * 2 * 2.

To evaluate this expression, we start by multiplying 2 by 2, then multiply the result by another 2, and finally multiply the final result by 1/100.

2 * 2 = 4,
4 * 2 = 8,
8 * (1/100) = 8/100 = 0.08 inch.

So, the total thickness of 2^3 sheets of 67-pound paper is 0.08 inch.

I hope this explanation helps! Let me know if you have any further questions or need more assistance.