Question

question
which expression is equivalent to \\(\frac{2^2}{2^3} \times 2^5\\)?

answer
\\(\frac{1}{16}\\) \\(\frac{1}{64}\\) 8 16

Explanation:

Step1: Simplify the fraction using exponent rule

Recall the exponent rule $\frac{a^m}{a^n}=a^{m - n}$. For $\frac{2^2}{2^3}$, we have $m = 2$ and $n=3$, so $\frac{2^2}{2^3}=2^{2 - 3}=2^{-1}$.

Step2: Multiply with the other term using exponent rule

Recall the exponent rule $a^m\times a^n=a^{m + n}$. Now we multiply $2^{-1}$ with $2^5$. So $2^{-1}\times2^5=2^{-1 + 5}=2^{4}$.

Step3: Calculate the value of $2^4$

We know that $2^4 = 2\times2\times2\times2=16$.

Answer:

16