Evaluate (5×6×7)/(9×11×13) Raised to Power b: Complex Fraction Expression

Question

Insert the corresponding expression:

(5×6×79×11×13)b= \left(\frac{5\times6\times7}{9\times11\times13}\right)^b=

Video Solution

Solution Steps

00:00 Simply
00:04 According to the laws of exponents, any fraction with power (N)
00:09 equals the numerator and denominator with the same power (N)
00:13 Note that both numerator and denominator are products
00:17 We will use this formula in our exercise
00:22 According to the laws of exponents when the entire product is to power (N)
00:26 equals each factor in the product separately raised to the same power (N)
00:32 We will use this formula in our exercise
00:48 And this is the solution to the question

Answer

5b×6b×7b9b×11b×13b \frac{5^b\times6^b\times7^b}{9^b\times11^b\times13^b}

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Power of a Quotient

Question Types

Powers of a Fraction: Variable in the exponent of the power Powers of a Fraction: System of equations with no solution