Question

Perform all the steps to evaluate this expression: ((6⁷/3³) div (6⁶/3⁴)³). What is the value of the expression?

a) one-eighth
b) One-half

Answer 1

The simplified expression (((6^7/3^3) div (6^6/3^4)^3)) reduces to 2/9 after evaluating exponents, performing division, and canceling out common terms. The value 2/9 is not one of the provided options.

Step-by-step explanation:

Let's simplify the given expression step by step:

(((6⁷/3³) div (6⁶/3⁴)³)

First, we evaluate the exponents and division inside the parentheses:

6⁷ means 6 multiplied by itself 7 times and 3³ means 3 multiplied by itself 3 times.
Similarly, 6⁶ means 6 multiplied by itself 6 times and 3⁴ means 3 multiplied by itself 4 times.

So the expression simplifies to:

(6× 6× 6× 6× 6× 6× 6) / (3× 3× 3)

And after simplifying the denominator of the second fraction:

(6× 6× 6× 6× 6× 6) / (3× 3× 3× 3)

Now, we use the property that (a·b)³ = a³·b³ to expand the cube of the second fraction:

((6⁷/3³) div ((6⁶³)/(3⁴³)))

Which gives:

((6⁷/3³) div (6¹¹/3¹¹) )

Since 6⁷ = 6× 6⁶ and 3¹¹ = 3× 3¹ and the div operator between the fractions signifies division, we can simplify further:

(6×(6⁶/3³)) / (6⁶/3⁴³) )

This simplifies by canceling out the common 6⁶ and 3³ terms leaving:

6 / 3¹ = 6 / 27

And since 6/27 can be simplified to 2/9, the final value of the expression is 2/9, which is not one of the options provided.