Question

which exponential expression is equivalent to \\(\sqrt8{z^7}\\)?
choose 1 answer:
a \\(z^{\frac{8}{7}}\\)
b \\(\frac{z^8}{z^7}\\)
c \\(\frac{z^7}{z^8}\\)
d \\(z^{\frac{7}{8}}\\)

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a radical to an exponential expression is $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. Here, $n = 8$ and $m=7$, and the base $a = z$.

Step2: Apply the rule to $\sqrt[8]{z^7}$

Using the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, substitute $n = 8$, $m = 7$, and $a=z$. So we get $z^{\frac{7}{8}}$.

Answer:

D. $z^{\frac{7}{8}}$