Equivalent expression

Question

The expression ³√27a^-6b³c² is equivalent to

(a) 3bc2/3 / a²

(b) 3b⁹c⁶ / a¹⁸

(c) 3b⁶c⁵ / a³

(d) 3b³√3c² / a²

Answer 1

Parentheses work great when the software falls short.

I will assume that the question is ³√(27a^-6b³c²). Does that format work for you/match your question?

First, we apply the Product Rule for Radicals... ³√(27a^-6b³c²) = ³√(27) • ³√(a^-6) • ³√(b³) • ³√(c²).

Next, we simplify each piece (factor)... 3 • a^-2 • b • ³√(c²)

Now we simplify the expression to get 3a^-2b ³√(c²) [The space between the b and the ³ is for clarity.]

Finally, we apply the Negative Exponent Rule and have (3b ³√(c²))/a².

The negative exponent means we have a denominator of a², which eliminates choices b & c.

The coefficient of the c is clearly 1, so the answer is a.

The radical is written as a rational exponent, so we have (3bc2/3)/a2.

Again, the parentheses make a big difference and hopefully make the statement more clear.