Question

Consider the equation (x^m)3=(x^13)^5*(x^-8)^-5
the value of m is
a.15
b.28
c.35
d.70

Answer 1

The answer will be 35

Answer 2

Answer:

Option C is correct.

The value of m for the given equation is, 35

Step-by-step explanation:

Given an equation:  $(x^m)^3=(x^{13})^5*(x^{-8})^{-5}$

To multiply the power of pwer, multiply the exponents on both sides of an equation:

$x^{3m}=(x^{65})*(x^{40})$       ...[1]

Using Property: When multiplying powers with the same base, then add the exponents.

Use the above property on  RHS in equation [1];

Since the base are same i.e, x ; we can add the exponents.

$x^{3m}=x^{65+40}$ or

$x^{3m}=x^{105}$

Using: $x^a=x^b$ , then a=b.

Therefore, 3m=105.

Divide 3 on both sides of an equation:

$\frac{3m}{3} =\frac{105}{3}$

Simplify:

m=35

Therefore, the valur of m is, 35.