Question

Given the equation (xm)^3=(x^13)^5×x^−8−5, find the value of m. Is it:

A) 15
B) 28
C) 35
D) 70

Answer 1

To find the value of m in the equation (xm)^3=(x^13)^5×x^−8−5, we can simplify it step by step, setting the exponents equal to each other and solving for m. The value of m is approximately 17.33.

Step-by-step explanation:

To find the value of m in the equation (xm)3 = (x13)5 × x-8-5, we can simplify it step by step:

1. Apply the power rule of exponents to simplify the right side of the equation: (x13)5 × x-8-5 = x13×5 × x-13 = x65 × x-13 = x65-13 = x52
2. Since the left side and the right side of the equation are equal, we can set the exponents equal to each other: m × 3 = 52
3. Now, solve for m by dividing both sides of the equation by 3: m = 52/3

The value of m is approximately 17.33, so none of the given options (A, B, C, D) represents the correct answer.