Question

I WILL GIVE 50 POINTS EACH TO WHOEVER SOLVES THIS!!!

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

Answer 1

2 ⁻³

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

Answer 2

• 2^-3

Explanation:

Solving in steps

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

• 4^−6 ⋅ 4^4⋅ (2^3⋅ 2^−4)^−1 =
• 4^(-6 + 4) ⋅ (2^(3 - 4))^-1 =
• 4^-2 ⋅ (2^(-1))^-1 =
• (2^2)^-2 ⋅ 2^((-1) ⋅ (-1)) =
• 2^-4 ⋅ 2^1 =
• 2^(-4 + 1) =
• 2^-3