Evaluate (6/11×13×15)^xy: Complex Fraction with Variable Exponents

Question

Insert the corresponding expression:

(611×13×15)xy= \left(\frac{6}{11\times13\times15}\right)^{xy}=

Video Solution

Solution Steps

00:12 Let's simplify this problem together!
00:15 Remember, according to the exponent rules, when a fraction is raised to the power of N,
00:21 both the top and bottom of the fraction are raised to this power.
00:25 We'll use this idea in our exercise.
00:38 Now, when a product is raised to the power of N,
00:42 each part of the product is raised to this same power.
00:48 We're going to apply this step to our example.
00:58 And there you have it, that's the solution!

Step-by-Step Solution

First, let's apply the exponent to the entire fraction:

(611×13×15)xy=6xy(11×13×15)xy \left(\frac{6}{11 \times 13 \times 15}\right)^{xy} = \frac{6^{xy}}{(11 \times 13 \times 15)^{xy}}

Now, distribute the xy xy exponent in the denominator to each factor:

6xy11xy×13xy×15xy \frac{6^{xy}}{11^{xy} \times 13^{xy} \times 15^{xy}}

Thus, the rewritten expression is 6xy11xy×13xy×15xy \frac{6^{xy}}{11^{xy} \times 13^{xy} \times 15^{xy}} .

Comparing our expression with the options given and based on our simplification, option 3: 6xy(11×13×15)xy \frac{6^{xy}}{\left(11 \times 13 \times 15\right)^{xy}} makes sense, as well as option 2: 6xy11xy×13xy×15xy \frac{6^{xy}}{11^{xy}\times13^{xy}\times15^{xy}} after distributing the exponent within the denominator.

Therefore, both options B and C are correct, making the right choice option 4.

Therefore, the correct answer is: B+C are correct.

Answer

B+C are correct