Two questions regarding exponents
$begingroup$
Question #1:
$$frac{frac{x^{2}y^{-3}}{3z^{{2}}} - frac{z^{-3}y^{-3}}{3x^{2}}}{frac{x^{-4}y^{2}}{3z^{-2}}}$$
Question #2:
$$(x^{-1} + y^{-1})^{-1}$$
Answer to Question #1:
$$frac{x^{6}z - x^{2}}{y^{5}z^{5}}$$
Answer to Question #2:
$$frac{xy}{x + y}$$
These questions are from the book Just in Time Algebra & Trig for Calculus, Section 1.4.
I am not able to reach the final answer for both of these problems, and I could use some help. And if you can clarify which "laws of exponents" are being used as well, because the second question above seems easy but I can't get the answer.
Thanks.
algebra-precalculus
asked Dec 23 '18 at 17:36
nooranoora
1
$endgroup$
add a comment |
$begingroup$
Question #1:
$$frac{frac{x^{2}y^{-3}}{3z^{{2}}} - frac{z^{-3}y^{-3}}{3x^{2}}}{frac{x^{-4}y^{2}}{3z^{-2}}}$$
Question #2:
$$(x^{-1} + y^{-1})^{-1}$$
Answer to Question #1:
$$frac{x^{6}z - x^{2}}{y^{5}z^{5}}$$
Answer to Question #2:
$$frac{xy}{x + y}$$
These questions are from the book Just in Time Algebra & Trig for Calculus, Section 1.4.
I am not able to reach the final answer for both of these problems, and I could use some help. And if you can clarify which "laws of exponents" are being used as well, because the second question above seems easy but I can't get the answer.
Thanks.
algebra-precalculus
asked Dec 23 '18 at 17:36
nooranoora
1
$endgroup$
$begingroup$
to answer your question as to which exponent rules to use, use these: $x^a = frac{1}{x^{-a}}$ ; $x^{-a} = frac{1}{x^a}$ ; $x^a cdot x^b = x^{a+b}$ ; $(x^a)^b = x^{a cdot b}$ ;
$endgroup$
– Hossien Sahebjame
Dec 23 '18 at 17:55
add a comment |
$begingroup$
Question #1:
$$frac{frac{x^{2}y^{-3}}{3z^{{2}}} - frac{z^{-3}y^{-3}}{3x^{2}}}{frac{x^{-4}y^{2}}{3z^{-2}}}$$
Question #2:
$$(x^{-1} + y^{-1})^{-1}$$
Answer to Question #1:
$$frac{x^{6}z - x^{2}}{y^{5}z^{5}}$$
Answer to Question #2:
$$frac{xy}{x + y}$$
These questions are from the book Just in Time Algebra & Trig for Calculus, Section 1.4.
I am not able to reach the final answer for both of these problems, and I could use some help. And if you can clarify which "laws of exponents" are being used as well, because the second question above seems easy but I can't get the answer.
Thanks.
algebra-precalculus
asked Dec 23 '18 at 17:36
nooranoora
1
$endgroup$
Question #1:
$$frac{frac{x^{2}y^{-3}}{3z^{{2}}} - frac{z^{-3}y^{-3}}{3x^{2}}}{frac{x^{-4}y^{2}}{3z^{-2}}}$$
Question #2:
$$(x^{-1} + y^{-1})^{-1}$$
Answer to Question #1:
$$frac{x^{6}z - x^{2}}{y^{5}z^{5}}$$
Answer to Question #2:
$$frac{xy}{x + y}$$
These questions are from the book Just in Time Algebra & Trig for Calculus, Section 1.4.
I am not able to reach the final answer for both of these problems, and I could use some help. And if you can clarify which "laws of exponents" are being used as well, because the second question above seems easy but I can't get the answer.
Thanks.
algebra-precalculus
algebra-precalculus
asked Dec 23 '18 at 17:36
nooranoora
1
asked Dec 23 '18 at 17:36
nooranoora
1
asked Dec 23 '18 at 17:36
nooranoora
1
asked Dec 23 '18 at 17:36
nooranoora
1
asked Dec 23 '18 at 17:36
nooranoora
1
1
$begingroup$
to answer your question as to which exponent rules to use, use these: $x^a = frac{1}{x^{-a}}$ ; $x^{-a} = frac{1}{x^a}$ ; $x^a cdot x^b = x^{a+b}$ ; $(x^a)^b = x^{a cdot b}$ ;
$endgroup$
– Hossien Sahebjame
Dec 23 '18 at 17:55
add a comment |
$begingroup$
to answer your question as to which exponent rules to use, use these: $x^a = frac{1}{x^{-a}}$ ; $x^{-a} = frac{1}{x^a}$ ; $x^a cdot x^b = x^{a+b}$ ; $(x^a)^b = x^{a cdot b}$ ;
$endgroup$
– Hossien Sahebjame
Dec 23 '18 at 17:55
$begingroup$
to answer your question as to which exponent rules to use, use these: $x^a = frac{1}{x^{-a}}$ ; $x^{-a} = frac{1}{x^a}$ ; $x^a cdot x^b = x^{a+b}$ ; $(x^a)^b = x^{a cdot b}$ ;
$endgroup$
– Hossien Sahebjame
Dec 23 '18 at 17:55
$begingroup$
to answer your question as to which exponent rules to use, use these: $x^a = frac{1}{x^{-a}}$ ; $x^{-a} = frac{1}{x^a}$ ; $x^a cdot x^b = x^{a+b}$ ; $(x^a)^b = x^{a cdot b}$ ;
$endgroup$
– Hossien Sahebjame
Dec 23 '18 at 17:55
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Hint to your first Question:
Write
$$frac{x^2}{3z^2y^2}-frac{1}{3x^2y^3z^3}=frac{x^4z}{3x^2y^3z^3}-frac{1}{3x^2y^3z^3}$$
and you will get
$$frac{(x^4z^2-1)}{3x^2y^3z^3}cdot frac{3x^4}{y^2z^2}$$
The result should be $$frac{x^2 left(x^4 z-1right)}{y^5 z^5}$$
answered Dec 23 '18 at 17:41
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Hint to your first Question:
Write
$$frac{x^2}{3z^2y^2}-frac{1}{3x^2y^3z^3}=frac{x^4z}{3x^2y^3z^3}-frac{1}{3x^2y^3z^3}$$
and you will get
$$frac{(x^4z^2-1)}{3x^2y^3z^3}cdot frac{3x^4}{y^2z^2}$$
The result should be $$frac{x^2 left(x^4 z-1right)}{y^5 z^5}$$
answered Dec 23 '18 at 17:41
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
$endgroup$
add a comment |
$begingroup$
Hint to your first Question:
Write
$$frac{x^2}{3z^2y^2}-frac{1}{3x^2y^3z^3}=frac{x^4z}{3x^2y^3z^3}-frac{1}{3x^2y^3z^3}$$
and you will get
$$frac{(x^4z^2-1)}{3x^2y^3z^3}cdot frac{3x^4}{y^2z^2}$$
The result should be $$frac{x^2 left(x^4 z-1right)}{y^5 z^5}$$
answered Dec 23 '18 at 17:41
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
$endgroup$
add a comment |
$begingroup$
Hint to your first Question:
Write
$$frac{x^2}{3z^2y^2}-frac{1}{3x^2y^3z^3}=frac{x^4z}{3x^2y^3z^3}-frac{1}{3x^2y^3z^3}$$
and you will get
$$frac{(x^4z^2-1)}{3x^2y^3z^3}cdot frac{3x^4}{y^2z^2}$$
The result should be $$frac{x^2 left(x^4 z-1right)}{y^5 z^5}$$
answered Dec 23 '18 at 17:41
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
$endgroup$
Hint to your first Question:
Write
$$frac{x^2}{3z^2y^2}-frac{1}{3x^2y^3z^3}=frac{x^4z}{3x^2y^3z^3}-frac{1}{3x^2y^3z^3}$$
and you will get
$$frac{(x^4z^2-1)}{3x^2y^3z^3}cdot frac{3x^4}{y^2z^2}$$
The result should be $$frac{x^2 left(x^4 z-1right)}{y^5 z^5}$$
answered Dec 23 '18 at 17:41
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
edited Dec 23 '18 at 17:51
answered Dec 23 '18 at 17:41
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
answered Dec 23 '18 at 17:41
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
answered Dec 23 '18 at 17:41
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
77.4k42866
add a comment |
add a comment |
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$begingroup$
to answer your question as to which exponent rules to use, use these: $x^a = frac{1}{x^{-a}}$ ; $x^{-a} = frac{1}{x^a}$ ; $x^a cdot x^b = x^{a+b}$ ; $(x^a)^b = x^{a cdot b}$ ;
$endgroup$
– Hossien Sahebjame
Dec 23 '18 at 17:55