Assume that no variable equals 0

1. c^12•c^-4•c^6
2. b^8/b^2
3. (a^4)^5
4. x^-2y/x^4y^-1
5. (a^2b/a^-3b^2)^-1
6. (x^2y/xy^3)^2
7. 1/2(-5a^2b^3)^2(abc)^2
8. m^7•m^8
9. 8m^3n^2/4mn^3
10. 2^3c^4t^2/2^2c^4t^2

help me please !

Step-by-step explanation:

When you multiply exponents of the same base (variable), add the exponents.

1. The exponents are 12 - 4 + 6 = 14 or c^14

When you divide exponents of the same base, subtract them.

2. 8 - 2 = 6 or c^6

When you raise a power to a power, you multiply the exponents.

3. 4 * 5 = 20 or c^20

When a number is raised to a negative exponent it can be re written like this x^-n = 1/x^n.

4. x^-2 * y / x^4 * y^-1; using the above information, rewrite everything to have positive exponents. If the negative exponent is in the denominator, then it becomes x^n/1

y * y / x^2 * x^4 ; then just add your exponents to simplify

y^2 / x^6

As we said before, a power raised to a power is exponent x exponent.

5. (a^2 * b) ^-1 / (a^-3 * b^2)^-1 ; as before a power raised to a power, multiply the powers.

a^-2 * b-1 / a^3 * b^-2 rewrite this as before, inverting negative exponents. a^3 / a^2 * b^1 * b^2 = a^3 / a^2 * b^3

Simolifynthe new expression to reduce the a variable by subtracting the bottom a^2 from the top a^3 and are left with

a / b^3

Work number 6 like 5, no negative exponents, so there won't be any inversions. Just multiply the outside power times every exponent, then do the division by subtracting exponents of like bases.

When figuring out the problems with constants, treat them like the variables. In number 7 the 5a^2 when raised to the 2nd power would be 5^2*(a^2)^2 = 25 a^4

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x
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1
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