Answer:
[tex]2^{8}\cdot 2^{\frac{2}{10}}\cdot 2^{\frac{4}{100}}[/tex]
B is correct
Step-by-step explanation:
Given: [tex]2^{8.24}[/tex]
Using exponent law,
[tex]x^{a+b}=x^a\cdot x^b[/tex]
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 )
[tex]8.24=8+.2+.04[/tex]
[tex]8.24=8+\dfrac{2}{10}+\dfrac{4}{100}[/tex]
[tex]2^{8.24}=2^{8+\frac{2}{10}+\frac{4}{100}}[/tex]
Using exponent law
[tex]2^{8.24}=2^{8}\cdot 2^{\frac{2}{10}}\cdot 2^{\frac{4}{100}}[/tex]
Hence, The equivalent expression is [tex]2^{8}\cdot 2^{\frac{2}{10}}\cdot 2^{\frac{4}{100}}[/tex]
