Math Summer Packet help?

Question

my mom only JUST decided to give me my summer review packet...but i dont remember anything...can u pleeeeeaaaaasee help out?

SIMPLIFY:

(-2)^-4 ?

(17x^15y^-3/3x^-4y^-2)^0

SOLVE:

4[3(6-t)-4(5+2t)]-12*greater then or equal to* -2[3(4+3t)-1]

thoose are the ones im confused about...

it'd would be awesome if you explained how too...

best answer 10 points!

Answer 1

SIMPLIFY:

(-2)^-4...the negative exponent means to switch the numerator and denominator:

(1/-2)^4...take each part to the power of 4:

1^4/-2^4...multiply each one out:

(1)(1)(1)(1)/(-2)(-2)(-2)(-2)

1/16

(17x^15y^-3/3x^-4y^-2)^0

Anything to the power of 0 equals 1...so the answer is 1

4[3(6-t)-4(5+2t)]-12>= -2[3(4+3t)-1]

Use the distributive property, one part at a time:

4[18 - 3t + -20 - 8t] - 12 >= -2[12 + 9t - 1]

Combine like terms inside parentheses:

4[-11t + -2] - 12 >= -2[11 + 9t]

Distribute again:

-44t + -8 - 12 >= -22 + -18t

Combine like terms:

-44t + -20 >= -22 + -18t

Add 20 to both sides:

-44t >= -2 + -18t

Add 18t to both sides:

-26t >= -2

Divide both sides by -26 (switch >= to <= since we are multiplying or dividing by a negative number):

t <= 2/26

Simplify the fraction:

t <= 1/13

Hope that helps!