Write each of the following expressions as a powers of 2: 4^−6⋅ 4^4⋅ (2^3⋅ 2^−4)^−1

Step-by-step explanation:

Solving in steps

Using exponent rules: a^b·a^c = a^(b+c) and (a^b)^c = a^(bc)

Step-by-step explanation:

the expression 4^−6⋅ 4^4⋅ (2^3⋅ 2^−4)^−1 can be solved using exponential rule:

= 4⁻⁶ * 4⁴ * (2³ * 2⁻⁴)⁻¹

= 4⁽⁻⁶ ⁺ ⁴⁾ * (2 ⁽³ ⁻ ⁴⁾ ) ⁻¹

= 4⁻² * (2⁻¹)⁻¹

= (2²) ⁻² * 2 ⁽⁻¹ ˣ ⁻¹⁾

= 2⁻⁴ * 2¹

= 2 ⁽⁻⁴ ⁺ ¹⁾

= 2 ⁻³

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.