Solve for t 78/174=65/145*(porportion)

Math
78174=65145⋅(porportion)
Rewrite the equation as 65145⋅(porportion)=78174.
65145⋅(porportion)=78174
Multiply both sides of the equation by 165145⋅i.
165145⋅i⋅65145⋅(porportion)=165145⋅i⋅78174
Simplify both sides of the equation.
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Simplify 165145⋅i⋅65145⋅(porportion).
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Multiply p by p by adding the exponents.
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Move p.
165145⋅i⋅65145⋅(p⋅porortion)=165145⋅i⋅78174
Multiply p by p.
165145⋅i⋅65145⋅(p2orortion)=165145⋅i⋅78174
165145⋅i⋅65145⋅(p2orortion)=165145⋅i⋅78174
Multiply o by o by adding the exponents.
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Move o.
165145⋅i⋅65145⋅(p2(o⋅o)r⋅rtion)=165145⋅i⋅78174
Multiply o by o.
165145⋅i⋅65145⋅(p2o2r⋅rtion)=165145⋅i⋅78174
165145⋅i⋅65145⋅(p2o2r⋅rtion)=165145⋅i⋅78174
Multiply o2 by o by adding the exponents.
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Move o.
165145⋅i⋅65145⋅(p2(o⋅o2)r⋅rtin)=165145⋅i⋅78174
Multiply o by o2.
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Raise o to the power of 1.
165145⋅i⋅65145⋅(p2(o1o2)r⋅rtin)=165145⋅i⋅78174
Use the power rule aman=am+n to combine exponents.
165145⋅i⋅65145⋅(p2o1+2r⋅rtin)=165145⋅i⋅78174
165145⋅i⋅65145⋅(p2o1+2r⋅rtin)=165145⋅i⋅78174
Add 1 and 2.
165145⋅i⋅65145⋅(p2o3r⋅rtin)=165145⋅i⋅78174
165145⋅i⋅65145⋅(p2o3r⋅rtin)=165145⋅i⋅78174
Multiply r by r by adding the exponents.
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Move r.
165145⋅i⋅65145⋅(p2o3(r⋅r)tin)=165145⋅i⋅78174
Multiply r by r.
165145⋅i⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
165145⋅i⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
Combine 65145 and i.
165i145⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
Reduce the expression 65i145 by cancelling the common factors.
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Factor 5 out of 65i.
15(13i)145⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
Factor 5 out of 145.
15(13i)5(29)⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
Cancel the common factor.
15(13i)5⋅29⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
Rewrite the expression.
113i29⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
113i29⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
Multiply the numerator by the reciprocal of the denominator.
12913i⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
Multiply 2913i by 1.
2913i⋅65145⋅(p2o3r2tin)=165145⋅i⋅78174
Cancel the common factor of 29.
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Factor 29 out of 145.
2913i⋅6529(5)⋅(p2o3r2tin)=165145⋅i⋅78174
Cancel the common factor.
2913i⋅6529⋅5⋅(p2o3r2tin)=165145⋅i⋅78174
Rewrite the expression.
113i⋅655⋅(p2o3r2tin)=165145⋅i⋅78174
113i⋅655⋅(p2o3r2tin)=165145⋅i⋅78174
Cancel the common factor of 13.
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Factor 13 out of 13i.
113(i)⋅655⋅(p2o3r2tin)=165145⋅i⋅78174
Factor 13 out of 65.
113(i)⋅13(5)5⋅(p2o3r2tin)=165145⋅i⋅78174
Cancel the common factor.
113i⋅13⋅55⋅(p2o3r2tin)=165145⋅i⋅78174
Rewrite the expression.
1i⋅55⋅(p2o3r2tin)=165145⋅i⋅78174
1i⋅55⋅(p2o3r2tin)=165145⋅i⋅78174
Multiply 1i and 55.
5i⋅5⋅(p2o3r2tin)=165145⋅i⋅78174
Cancel the common factor of i.
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Factor i out of i⋅5.
5i(5)⋅(p2o3r2tin)=165145⋅i⋅78174
Factor i out of p2o3r2tin.
5i(5)⋅(i(p2o3r2tn))=165145⋅i⋅78174
Cancel the common factor.
5i⋅5⋅(i(p2o3r2tn))=165145⋅i⋅78174
Rewrite the expression.
55⋅(p2o3r2tn)=165145⋅i⋅78174
55⋅(p2o3r2tn)=165145⋅i⋅78174
Combine p2 and 55.
p2⋅55⋅(o3r2tn)=165145⋅i⋅78174
Combine o3 and p2⋅55.
o3(p2⋅5)5⋅(r2tn)=165145⋅i⋅78174
Combine r2 and o3(p2⋅5)5.
r2(o3(p2⋅5))5⋅(tn)=165145⋅i⋅78174
Combine t and r2(o3(p2⋅5))5.
t(r2(o3(p2⋅5)))5⋅n=165145⋅i⋅78174
Combine t(r2(o3(p2⋅5)))5 and n.
t(r2(o3(p2⋅5)))n5=165145⋅i⋅78174
Cancel the common factor of 5.
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Cancel the common factor.
t(r2(o3(p2⋅5)))n5=165145⋅i⋅78174
Divide t(r2(o3(p2)))n by 1.
t(r2(o3(p2)))n=165145⋅i⋅78174
tr2o3p2n=165145⋅i⋅78174
tr2o3p2n=165145⋅i⋅78174
Simplify 165145⋅i⋅78174.
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Combine 65145 and i.
tr2o3p2n=165i145⋅78174
Reduce the expression 65i145 by cancelling the common factors.
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Factor 5 out of 65i.
tr2o3p2n=15(13i)145⋅78174
Factor 5 out of 145.
tr2o3p2n=15(13i)5(29)⋅78174
Cancel the common factor.
tr2o3p2n=15(13i)5⋅29⋅78174
Rewrite the expression.
tr2o3p2n=113i29⋅78174
tr2o3p2n=113i29⋅78174
Multiply the numerator by the reciprocal of the denominator.
tr2o3p2n=12913i⋅78174
Multiply 2913i by 1.
tr2o3p2n=2913i⋅78174
Cancel the common factor of 29.
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Factor 29 out of 174.
tr2o3p2n=2913i⋅7829(6)
Cancel the common factor.
tr2o3p2n=2913i⋅7829⋅6
Rewrite the expression.
tr2o3p2n=113i⋅786
tr2o3p2n=113i⋅786
Cancel the common factor of 13.
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Factor 13 out of 13i.
tr2o3p2n=113(i)⋅786
Factor 13 out of 78.
tr2o3p2n=113(i)⋅13(6)6
Cancel the common factor.
tr2o3p2n=113i⋅13⋅66
Rewrite the expression.
tr2o3p2n=1i⋅66
tr2o3p2n=1i⋅66
Multiply 1i and 66.
tr2o3p2n=6i⋅6
Cancel the common factor of 6.
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Cancel the common factor.
tr2o3p2n=6i⋅6
Rewrite the expression.
tr2o3p2n=1i
tr2o3p2n=1i
Multiply the numerator and denominator of 1i by the conjugate of i to make the denominator real.
tr2o3p2n=1i⋅ii
Multiply.
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Combine.
tr2o3p2n=1iii
Multiply i by 1.
tr2o3p2n=iii
Simplify the denominator.
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Raise i to the power of 1.
tr2o3p2n=ii1i
Raise i to the power of 1.
tr2o3p2n=ii1i1
Use the power rule aman=am+n to combine exponents.
tr2o3p2n=ii1+1
Add 1 and 1.
tr2o3p2n=ii2
Rewrite i2 as -1.
tr2o3p2n=i-1
tr2o3p2n=i-1
tr2o3p2n=i-1
Move the negative one from the denominator of i-1.
tr2o3p2n=-1⋅i
Rewrite -1⋅i as -i.
tr2o3p2n=-i
tr2o3p2n=-i
tr2o3p2n=-i
Divide each term by r2o3p2n and simplify.
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Divide each term in tr2o3p2n=-i by r2o3p2n.
tr2o3p2nr2o3p2n=-ir2o3p2n
Simplify tr2o3p2nr2o3p2n.
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Cancel the common factor of r2.
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Cancel the common factor.
tr2o3p2nr2o3p2n=-ir2o3p2n
Rewrite the expression.
to3p2no3p2n=-ir2o3p2n
to3p2no3p2n=-ir2o3p2n
Cancel the common factor of o3.
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Cancel the common factor.
to3p2no3p2n=-ir2o3p2n
Rewrite the expression.
tp2np2n=-ir2o3p2n
tp2np2n=-ir2o3p2n
Cancel the common factor of p2.
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Cancel the common factor.
tp2np2n=-ir2o3p2n
Rewrite the expression.
tnn=-ir2o3p2n
tnn=-ir2o3p2n
Cancel the common factor of n.
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Cancel the common factor.
tnn=-ir2o3p2n
Divide t by 1.
t=-ir2o3p2n
t=-ir2o3p2n
t=-ir2o3p2n
Move the negative in front of the fraction.
t=-ir2o3p2n
t=-ir2o3p2n
Solve for t 78/174=65/145*(porportion)

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