Question

3) Which of the following expressions is equivalent to 2^5*(1/4)^7?

Answer 1

Given:

The expression;

`2^5*((1)/(4))^7`
`\begin{gathered} 2^5*((1)/(4))^7 \\ 2^5*(((1)/(2))^2)^7 \\ Apply\text{ing the index law of powers,} \\ (x^a)^b=x^(ab)^{} \\ 2^5*(((1)/(2))^2)^7=2^5*((1)/(2))^(14) \\ \\ \text{Thus,} \\ 2^5*((1)/(2))^(14)=2^5*(1^(14))/(2^(14)) \\ 2^5*(1^(14))/(2^(14))=2^5*\frac{1^{}}{2^(14)} \\ \\ \text{Applying the law of negative exponent,} \\ x^(-a)=(1)/(x^a) \\ 2^5*\frac{1^{}}{2^(14)}=2^5*2^(-14) \\ \\ \text{Apply ing the product law of indices,} \\ x^a* x^b=x^(a+b) \\ \\ \text{Hence, } \\ 2^5*2^(-14)=2^(5+(-14)) \\ 2^(5+(-14))=2^(5-14) \\ =2^(-9) \end{gathered}`

Therefore, the correct answer is OPTION C.