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

Tutors, sign in to answer this question.

Ryan S. | Mathematics and StatisticsMathematics and Statistics

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.

Juan C. | Physics, Math, Biology and Chemistry tutor.Physics, Math, Biology and Chemistry tut...

The answers for this questions are:

1- (x/2)^{7}= x^{7}/2^{7} = x^{7}/128

2- (4/13)^{0}= 1 --> because any number to a power of "0" is always 1

3- (m^{9}/n^{6})^{8}= m^{(9x8)}/n^{(6x8)}= m^{72}/n^{48 }--> when you have an exponent elevated to another exponent, you multiply them like I did this exercise

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Thomas E.

Improve Math and Reading Skills

$10 per 15 min

View Profile >

Kyoko I.

Native Japanese Speaker Fluent in English, Customized Teaching

$11.25 per 15 min

View Profile >

Alexis G.

All-Subject/Test Prep Tutor, Specializing in Language Instruction

$11.25 per 15 min

View Profile >