simplify the expressions...
1. (x^3)^5
2. (y^4)^5
3. 4^8/4^2(this is a fraction)
4. b^2/b^4(this is a fraction)
5. 28xy^7/32xy^12(this is a fraction)
Please show me step by step because I am not really understanding these types of problems...
Demanding HELP NOW won't work unless there happens to be a math tutor online at the moment. Stamping your feet for HELP NOW won't either.
Be sure you have read the instructions on the Post a New Question screen:
Homework Posting Tips
Please show your work. Tutors will not do your homework for you. Please show your work for any question that you are posting.
Please proofread your question. Does your question use proper grammar, capitalization, and spelling?
Please be patient. All tutors are volunteers, and sometimes a tutor may not be immediately available. Please be patient while waiting for a response to your question.
Wow...that was rude. I didn't mean to make it sound that way, I was just confused...
o_o sorry
If you demonstrate what you've done so far and/or where you think you're running into trouble, a math tutor will be able to help you better. They need to know what you know.
And please remember that when you use all caps online, it's as if you're SHOUTING at us. Just "Math" in the subject line is all you need to put -- or better, the class you're taking, such as Algebra 2 or Trig or something specific like that.
Okay, my bad, so sorry. I am just having a difficult time simplifying the expressions that involve fractions w/ exponents. I have my textbook and I have been working on it for awhile but I need more guidance on how to do it...I can be a slow learner sometimes. If you can help me that would be great, but I'm guessing you are not a math tutor. In the future, I won't use ALL CAPS. Sorry again...
To be able to handle these types of exponent questions, you must have been given the basic laws of exponents, or they will be found in your text or notes.
your first question matches the rule that
(a^x)^y = a^(xy)
so , (x^3)^5 = x^15
#2 is the same
#3, you will need a^x / a^y = a^(x-y)
#4 same thing
#5, think of it as
28xy^7/(32xy^12)
= (28/32)(x/x)(y^7/y^12)
= (7/8)(y^-5)
or
= (7/8)(1/y^5) or 7/(8y^5)
using the rule that a^-n = 1/a^n
Oh okay! That actually makes more sense...Thanks :)
Sure! I'll break down each expression step by step to help you understand how to simplify them.
1. To simplify (x^3)^5:
- Start by applying the power rule for exponents, which states that when raising a power to a power, you multiply the exponents. Therefore, (x^3)^5 becomes x^(3*5) = x^15.
2. To simplify (y^4)^5:
- Similar to the previous example, apply the power rule for exponents. (y^4)^5 becomes y^(4*5) = y^20.
3. To simplify 4^8/4^2:
- When dividing with the same base, you can apply the division rule for exponents, which states that you subtract the exponents. Therefore, 4^8/4^2 becomes 4^(8-2) = 4^6, resulting in the simplified expression 4^6.
4. To simplify b^2/b^4:
- For this fraction, you can apply the division rule for exponents. Subtract the exponent in the denominator from the exponent in the numerator. Therefore, b^2/b^4 becomes b^(2-4) = b^(-2).
- Now, if you have a negative exponent, you can rewrite it as the reciprocal of the positive exponent. In this case, b^(-2) can be written as 1/b^2. So, the simplified expression is 1/b^2.
5. To simplify (28xy^7)/(32xy^12):
- First, simplify the numerical part of the fraction by dividing both numbers by their greatest common divisor. In this case, the greatest common divisor of 28 and 32 is 4. So, the fraction becomes (7xy^7)/(8xy^12).
- Now, apply the division rule for exponents separately to the variables x and y. Divide the exponents of x (1 for the numerator and 1 for the denominator), which cancels out, leaving you with just x in both the numerator and denominator.
- For the variable y, subtract the exponents (7-12) to get y^(-5).
- Similar to the previous example, rewrite y^(-5) as 1/y^5.
- Therefore, the simplified expression is (7xy)/(8y^5).
I hope this step-by-step breakdown helps you understand how to simplify these types of expressions. Let me know if you have any further questions!