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Help with simplifying an expression with fractional & negative exponents!?
Please explain to me how to simplify the following expression. The answer = x / 9y^7
( [ 3 x^(3/2) y^(3) ] / [ x^(2) y^(- 1/2) ] ) ^-2
Clicking here to see a picture of it may be easier to understand:
2 Answers
- MaverickLv 710 years agoFavorite Answer
Some basic rules:
negative exponent => turn fraction upside down
multiply same variable by different exponents => add exponents
raise a power to a power => multiply powers
.. ( [ 3 x^(3/2) y^(3) ] / [ x^(2) y^(- 1/2) ] ) ^-2
= ( [ x^(2) y^(- 1/2) ] / [ 3 x^(3/2) y^(3) ] ) ^2
= ( [ x^(2) x^(-3/2) ] / [ 3 y^(3) y^(1/2) ] ) ^2
= ( [ x^(2 + -3/2) ] / [ 3 y^(3 + 1/2) ] ) ^2
= ( [ x^(1/2) ] / [ 3 y^(7/2) ] ) ^2
= [ x^(1/2) ]^2 / [ 3 y^(7/2) ]^2
= x^(1/2)^2 / 3^2 y^(7/2)^2
= x^(1/2 * 2) / 9 y^(7/2 * 2)
= x / 9y^7
Answered your question?
Source(s): Having taught A-level Maths - Anonymous5 years ago
((x+9)-(x+9)^5)^-1/4=((x+9)(1-(x+9)^4)^-...
