select the expression equivalent to $sqrt8{x^{77}}$ given $x 0$.
answer
$\circ$ $x^8\sqrt8{x^4}$ $\circ$ $x^8\sqrt8{x^5}$
$\circ$ $x^9\sqrt8{x^5}$ $\circ$ $x^9\sqrt8{x^4}$

Question

select the expression equivalent to $sqrt8{x^{77}}$ given $x > 0$.
answer
$\circ$ $x^8\sqrt8{x^4}$ $\circ$ $x^8\sqrt8{x^5}$
$\circ$ $x^9\sqrt8{x^5}$ $\circ$ $x^9\sqrt8{x^4}$

Accepted Answer

# Explanation:
## Step1: Rewrite exponent as quotient/remainder
Divide 77 by 8: $77 = 8	imes9 + 5$
## Step2: Split radical using exponent rule
$\sqrt[8]{x^{77}} = \sqrt[8]{x^{8	imes9} \cdot x^5}$
## Step3: Simplify radical expression
$\sqrt[8]{x^{8	imes9} \cdot x^5} = \sqrt[8]{x^{8	imes9}} \cdot \sqrt[8]{x^5} = x^9\sqrt[8]{x^5}$

# Answer:
$x^9\sqrt[8]{x^5}$

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QUESTION IMAGE

Question

Explanation:

Step1: Rewrite exponent as quotient/remainder

Step2: Split radical using exponent rule

Step3: Simplify radical expression

Answer: