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

Option C is correct.

The value of m for the given equation is, 35

Step-by-step explanation:

Given an equation:  

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

      ...[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.

or

Using: , then a=b.

Therefore, 3m=105.

Divide 3 on both sides of an equation:

Simplify:

m=35

Therefore, the valur of m is, 35.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: