Answer:
The choice [tex]2^{6}.2^{3/10}.2^{8/100}[/tex] is equivalent to the expression [tex]2^{6.38}[/tex] ⇒ A
Step-by-step explanation:
Let us revise some rules of exponents
- [tex]a^{n}.a^{m}=a^{n+m}[/tex]
- [tex]\frac{a^{n} }{a^{m}}=a^{n-m}[/tex]
- [tex](a^{n})^{m}=a^{nm}[/tex]
Remember 1.23 can be written as 1 + [tex]\frac{2}{10}[/tex] + [tex]\frac{3}{100}[/tex]
∵ The expression is [tex]2^{6.38}[/tex]
- Write the exponent as a sum of its digits
∵ 6.38 = 6 + [tex]\frac{3}{10}[/tex] + [tex]\frac{8}{100}[/tex]
∴ The expression can be written as [tex](2)^{6+\frac{3}{10}+\frac{8}{100}}[/tex]
- We can change the adding of exponents to the product of the
same base as the 1st rule above product
∴ [tex](2)^{6+\frac{3}{10}+\frac{8}{100}}[/tex] = [tex](2)^{6}.(2)^{\frac{3}{10}}.(2)^{\frac{8}{100}}[/tex]
∴ [tex]2^{6.38}[/tex] = [tex](2)^{6}.(2)^{\frac{3}{10}}.(2)^{\frac{8}{100}}[/tex]
The choice [tex]2^{6}.2^{3/10}.2^{8/100}[/tex] is equivalent to the expression [tex]2^{6.38}[/tex]
