Question

Use properties of exponents to rewrite the following expressions as a number or an exponential expression with only one exponen.

[(√2)^√2]^√2

Answer 1

[(√2)^√2]^√2 = 2¹ = 2

Explanation:

Hi there!

Let´s write the expression:

[(√2)^√2]^√2

Now let´s rewrite it using fractional exponents (√2 = 2^1/2):

[(2^1/2)^2^1/2]^2^1/2

Let´s use the following property of exponents: (xᵃ)ᵇ = xᵃᵇ and multiply the exponents:

1/2 · 2^1/2 · 2^1/2

Now, let´s use the following property of exponents: xᵃ · xᵇ = xᵃ⁺ᵇ

1/2 · 2^(1/2 + 1/2) = 1/2 · 2¹ = 1

Then, the expression can be written as:

[(√2)^√2]^√2 = 2¹ = 2

Have a nice day!