i am having trouble understaing how to write these out in simplest form please help

a. 7^3x7^2x8^5/ 8^4x7x8^-7 for this i got 7/8

b. (a^-2b^4c^3)2

can you explain and show me how to do this?

I am having trouble understanding what you mean for part a. Is the x a variable or are you writing it as a times sign to indicate multiplication?

for b I am a little confused too.

a raised to the -2
b raised to the 4
c raised to the 3

should everything in the ( ) be squared?

if so the a^-4 the b^8 and c^6

you should never leave an answer with a negative exponent. You can move it to the denominator of the fraction and make it a^4. Keep the b and c with their exponents in the numerator.

yes they should be.... so that would make sense what about the first equation?

and part a iswhere x is the multiplication.

Checking with what I think you have in your problem

7^3 times 7^2 times 8^5 in the numerator?

If so you can simplify to 7^5 times 8^5 in the numerator

The denominator: 8^4 times 7 times 8^-7
if so you can simplify the denominator to 8^-3 times 7

7^5 times 8^5 divided by 8^-3 times 7

take 7^5 divided by 7^1 gives me 7^4

take 8^5 divided by 8^-3 gives me
8^(5+3) or 8 ^8

I think my final answeris 7^4 times 8^8

a. To simplify the expression 7^3 * 7^2 * 8^5 / 8^4 * 7 * 8^-7, we can start by simplifying the terms with the same base.

1. Start by evaluating the powers of 7: 7^3 * 7^2 = 7^(3+2) = 7^5.

So the expression becomes: 7^5 * 8^5 / 8^4 * 7 * 8^-7.

2. Now let's deal with the powers of 8: 8^5 / 8^4 = 8^(5-4) = 8^1 = 8.

The expression becomes: 7^5 * 8 / 7 * 8^-7.

3. Next, let's simplify the terms with the same bases of 7: 7^5 / 7 = 7^(5-1) = 7^4.

The expression further simplifies to: 7^4 * 8 / 8^-7.

4. Finally, deal with the powers of 8: 8/8^-7 = 8^1 * 8^7 = 8^(1+7) = 8^8.

Therefore, the simplest form of the expression is 7^4 * 8^8.

b. The expression (a^-2b^4c^3)2 can be simplified by multiplying the exponents outside the bracket with the exponents inside the bracket.

1. Start by applying the exponent outside the bracket to each term inside:
(a^-2)^2 * (b^4)^2 * (c^3)^2.

2. Simplify each term inside the bracket:
(a^-2)^2 = a^(-2 * 2) = a^-4.
(b^4)^2 = b^(4 * 2) = b^8.
(c^3)^2 = c^(3 * 2) = c^6.

3. Now, the simplified expression becomes:
a^-4 * b^8 * c^6.

Note: An exponent of -4 means to take the reciprocal of the base raised to the power of 4. So, a^-4 = 1/a^4.

The final simplest form of the expression is:
1/a^4 * b^8 * c^6.