Question

GUY HELP ME I CANT DO IT AND I ONLY HAVE ONE SHOT AT DOING IT AND MY GRADES ARE AT STEAK HERE PLEASE HELP ME

1. What is the value of the expression 7^–3?

A.
–21

B.
- 1/343

C.
1/343

D.
343

2. What is the value of the expression 1/3^-5 ?

A.
243

B.
15

C. 1/15


D. 1/243

3. What is the value of the expression 2/4^-3 ?

A. 1/32


B. 1/6


C.
128

D.
256

4. What value of k solves the equation?

K^-5 = 1/32

k = ?

5. What value of m solves the equation?

2^m = 1/8

m = ?

Answer 1

1) is -21 if you multiply -3x7 the answer is -21

Answer 2

1) 7⁻³ = 7 * 7 * 7 = 343 but because the exponent is negative
343/1 becomes 1/343. Letter C.
2) 1/3 ⁻⁵ = 1/3 * 1/3 * 1/3 * 1/3 * 1/3 = 1*1*1*1*1 / 3*3*3*3*3 = 1/15 since negative exponent ⇒ 1/15 becomes 1 ÷ 1/15. Remember the rules of division. multiply the 1st fraction to the reciprocal of the 2nd fraction.
1 ÷ 1/15 = 1 * 15/1 = 15 Letter B.
3) 2/4 ⁻³ = 2/4 * 2/4 * 2/4 = 2*2*2 / 4*4*4 = 8/64 negative exponent 1 ÷ 8/64
Rules of dividing fractions:
1 ÷ 8/64 ⇒ 1 * 64/8 = 64/8 ⇒ 8 not included in the choices.
4) k ⁻⁵ = 1/32 * this means that 32 must undergo prime factorization to get the base. k = 2 ⇒ 2⁵ = 32 ; 2⁻⁵ = 1/32
5) 2^m = 1/8 ; m = -3 ⇒ 2³ = 8 ; 2⁻³ = 1/8