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

00:00 Simplify the following problem
00:03 According to the laws of exponents, a fraction raised to the power (N)
00:08 equals the numerator and denominator raised to the same power (N)
00:12 We will apply this formula to our exercise
00:26 According to the laws of exponents when a product is raised to the power (N)
00:30 it is equal to each factor in the product separately raised to the same power (N)
00:36 We will apply this formula to our exercise
00:46 This is 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