Question

Which choice is equivalent to the expression below?

Answer 1

B is your answer because if you check each one in the calculator B is the same as the expression and also 2^8 makes up the first part and the second half makes up the .24

Answer 2

Answer:

$2^{8}\cdot 2^{\frac{2}{10}}\cdot 2^{\frac{4}{100}}$

B is correct

Step-by-step explanation:

Given: $2^{8.24}$

Using exponent law,

$x^{a+b}=x^a\cdot x^b$

Expand exponent 8.24

Position of each digit:

8 ⇒ It is at tens place (1 x 8)

2 ⇒ It is at tenth place (1/10 x 2)

4 ⇒ It is at hundredth place (1/100 x 4 )

$8.24=8+.2+.04$

$8.24=8+\dfrac{2}{10}+\dfrac{4}{100}$

$2^{8.24}=2^{8+\frac{2}{10}+\frac{4}{100}}$

Using exponent law

$2^{8.24}=2^{8}\cdot 2^{\frac{2}{10}}\cdot 2^{\frac{4}{100}}$

Hence, The equivalent expression is $2^{8}\cdot 2^{\frac{2}{10}}\cdot 2^{\frac{4}{100}}$