Additional Notes: Recall from unit 9 that when bases are being multiplied, you keep the base and add the exponents. Now we are going to include expressions that contain a coefficient (remember, that is a number attached to, and in front of, a variable.) We are going to multiply the COEFFICIENTS, keep the base and add the exponents.

• 7x^8 * 7x^5 = 49x^13 The exponents are attached to the base of x, so x is the base we are going to keep. Just like before, since the x's are being multiplied, we have to add the exponents. Those 2 facts are the same as last unit. Now we also have 7's in front of each x. The 7 is not the base since the 7 has no exponent therefore it is just a number. When we have numbers with a * sign, it means to multiply them. We can rewrite the problem using the Commutative Property to make it easier to see (remember the Commutative Property states that we can multiply in any order.)

7x^8 * 7x^5 means 7 * x^8 * 7 * x^5. When we move terms, it becomes: 7 * 7 * x^8 * x^5. In the first part, 7*7=49. In the second part,

x^8 * x^5 = x^13. When we put the two answers together, we get 49x^13.

• 3x^-8 * 2x^5 = 6x^-3 because 3*2=6 and -8+5=-3 we would then get rid of the negative exponent by doing the reciprocal: 6/x^3. We only do the reciprocal to BASES with negative exponents. 6 does not get the -3 exponent (think about expanding the answer from 6x^-3 to 6 * x^-3.)
• 4y^8 * 2y^-5 = 8y^3 because 4*2=8 and 8+ -5= 8 - 5 = 3
• 9y^-8 * -11y^-5 = -99y^-13 because 9 * -11 = -99 and -8+-5=-13 we would then get rid of the negative exponent by doing the reciprocal: -99/y^13. We only do the reciprocal to BASES with negative exponents. -99 does not get the -13 exponent (think about expanding the answer from -99y^-13 to -99 * x^-13.) A coefficient, which again is just a number, can be negative. We only do the reciprocal to negative EXPONENTS.

Additional Notes: Recall from unit 9 that when bases are being raised to a power, you keep the base and multiply the exponents. Now we are going to include expressions that contain a coefficient (remember, that is a number attached to, and in front of, a variable.) We are going to RAISE THE COEFFICIENT TO THE OUTSIDE POWER, keep the base and add the exponents.

• (2x^8)^5 = 32x^40 because 2^5 = 32 and x*5=40 (You can think of 2x^8 as 2^1 * x^8. Then when we raise this to the outside power of 5, we multiply ALL exponents giving 2^5 * x^40. Simplify 2^5 = 32 and put the answers together to get 32x^40)
• (7x^-8)^2 = 49x^-16 because 7^2 = 49 and -8*2=-16 we would then get rid of the negative exponent by doing the reciprocal: 49/x^16. (We only do the reciprocal to BASES with negative exponents. 49 does not get the -16 exponent)
• (5x^8)^-3 = 1/125x^24 because 5^-3 = 1/125 (negative exponent) and 8 * -3 = -24 we would then get rid of the negative exponents by doing the reciprocal to each part since they both have negative exponents: 1/125x^24
• (6x^-8)^-2 = x^16/36 because 6^-2 = 1/36 (negative exponent) and -8 * -2 = 16. The x does not have a negative exponent so it stays in the numerator. Only the 6 moves down.

Additional Notes: Recall that when a number is attached to parentheses by multiplication, we apply the Distributive Property. It may be helpful to write out the products and simplify the individual problems (as in Classwork examples 1 and 2).

• 2x^3(3x^2 + 5x - 4) write out as 3 separate products:

2x^3 * 3x^2 2x^3 * 5x 2x^3 * -4 then follow the multiplication rules for each of the 3 sections (don't forget + and - signs)

6x^5 +10x^4 -8x^3 then put together with appropriate signs

6x^5 + 10x^4 - 8x^3

F 4/24 Multiplication Practice

**Google Form "Quiz" was due last Wednesday and "Test" was due last Friday. Scroll up to last week and complete them you have not yet done so!

Today you will be practicing your beginning multiplication. Log into Delta Math and complete assignment "8RDL Monomials 1"

It is due Sunday 4/26 at 8pm