Question

If x = 2⁸ and $x^x = 2^y$, then find the value of 'y'.

• A. $$1$$
• B. $$2^4$$
• C. $$2^{64}$$
• D. $$2^{11}$$

Answer 1

Answer:

$$2^{11}$$

$x = 2^8$

$x^x = 2^y$

$(2^{8})^{2^8}$

$(a^m)^n=a^{(m\times n)}$

so

$2^{8\times 2^8}$= $2^y$

$y=8\times 2^8$

$y=2^3 \times 2^8$

$a^m\times a^n=a^{m+n}$

$y=2^{11}$