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Property exponent .................................

Assumed that all variables are nonzero
 
(1) Simplify(x/2)^7
 
(2)simplify (4/13)^0
 
(3) Simplify (m^9/n^6)^8
 
I have solved the number 1 and 2 but am not sure if i got it right or now .
 
simplify (x/2)^7 =x^7/2^7 
                        =1/128^7
 
Simplify (4/13)^0=4^1/13^1
                        = (4/13)^=1
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2 Answers

For #1, you are correct to raise both the numerator and the denominator to the 7th power. x^7 cannot be expressed any other way since we do not know the value of x. It is not equal to one unless being raised to the zeroth power. You are right that 2^7=128 but you do not want to then raise 128 to the 7th power. The final expression is x^7/128.
 
For #2 your final answer is right. Any number raised to the zeroth power is 1. Your process is not correct, however. The result of raising the fraction 4/13 to the zeroth power is 4^0/13^0=1/1=1, not 4^1/13^1.
 
For #3, you need to raise both the numerator and the denominator to the 8th power. This involves raising a power to a power which requires multiplying exponents. The result is m^72/n^48.
The answers for this questions are: 
1- (x/2)7= x7/27 = x7/128
 
2- (4/13)0= 1 --> because any number to a power of "0" is always 1
 
3- (m9/n6)8= m(9x8)/n(6x8)= m72/n48 --> when you have an exponent elevated to another exponent, you                   multiply them like I did this exercise