Okay, here it is again.?

Question

Could someone please work this problem for me. If you don't know, just move on?

I'm having a problem figuring this one out. Any help would be appreciated. Thanks.

Please simplify:
6x^-6 t^6 x^9 * 3z^7 *4z^-7 t^-8

Please factor completely:
6t^4 + 21t^3 - 45t^2

Answer 1

1) To multiply exponential functions with the same base, just add the exponents together.

For example, you have a (x^-6) and a (x^9). Multiplied together, you get (x^3). You added a (-6) and (+9).

All of the coefficients (the numbers) can be multiplied together.

2) First step is to pull a t^2 out (Divide each term by t^2 - in other words, subtract 2 from each of the exponents). All of the coefficients are divisible by 3, so you can pull a 3 out. That leaves you with a quadratic equation.

3t^2*(2t^2 + 7t - 15)

One way to solve a quadratic equation is to use the quadratic formula. In this case, 2 can only be factored into 2 and 1, and 15 can only be factored into 3 and 5). You only have four combinations to pick from, so you can find the factors through trial and error faster than using the quadratic formula.

You could have:

(2t + 3) (t -5) except 2*(-5) = -10 and you'd wind up with a -7t instead of positive. If you swap the negative signs, it would surely work out.

(2t - 3)(t + 5) gives you a +10 and a (-3), or +7t which is what you want.

(2t + 5)(t - 3) gives you a -6 and +5, or a -t. You wanted +7t.

(2t - 5)(t + 3) gives you a +6 and a -5, or a +t. You wanted +7t.

So while you technically have four possibilities, two of those were just opposites of each other.

Your final answer would be:

3t^2 (2t - 3) (t + 5)

Answer 2

nylon freak; totally inappropriate
red night; if you're not good in math why answer?

1.
collect like terms, when multiplying exponents with like bases you add the exponents:

6x^-6 t^6 x^9 * 3z^7 *4z^-7 t^-8
= (6*1)x^(-6+9) (1*1)t^(6-8) (3*4)z^(7-7)
= 6x^3 t^-2 12

2.
6t^4 + 21t^3 - 45t^2
=3t^2 (2t^2 + 7t - 15)
= 3t^2 (2t^2 - 3t + 10t - 15)
= 3t^2 [t (2t-3) + 5(2t - 3)]
= 3t^2 (t+5) (2t -3)

Answer 3

The second one is:
3t^2 (2t^2 + 7t - 15)

It's been a while since i have had math so check with someone else before you use my answer, but i think it is right.

Answer 4

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Answer 5

AM NOT GOOD IN MATH SORRY