Combine (3v)/(8d^3k^2)-(5d^3u)/(12a^2k)

Math
3v8d3k2-5d3u12a2k
To write 3v8d3k2 as a fraction with a common denominator, multiply by 3a23a2.
3v8d3k2⋅3a23a2-5d3u12a2k
To write -5d3u12a2k as a fraction with a common denominator, multiply by 2d3k2d3k.
3v8d3k2⋅3a23a2-5d3u12a2k⋅2d3k2d3k
Write each expression with a common denominator of 24d3k2a2, by multiplying each by an appropriate factor of 1.
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Multiply 3v8d3k2 and 3a23a2.
3v(3a2)8d3k2(3a2)-5d3u12a2k⋅2d3k2d3k
Multiply 3 by 8.
3v(3a2)24d3k2a2-5d3u12a2k⋅2d3k2d3k
Multiply 5d3u12a2k and 2d3k2d3k.
3v(3a2)24d3k2a2-5d3u(2d3k)12a2k(2d3k)
Multiply 2 by 12.
3v(3a2)24d3k2a2-5d3u(2d3k)24a2k(d3k)
Raise k to the power of 1.
3v(3a2)24d3k2a2-5d3u(2d3k)24a2(d3(k1k))
Raise k to the power of 1.
3v(3a2)24d3k2a2-5d3u(2d3k)24a2(d3(k1k1))
Use the power rule aman=am+n to combine exponents.
3v(3a2)24d3k2a2-5d3u(2d3k)24a2(d3k1+1)
Add 1 and 1.
3v(3a2)24d3k2a2-5d3u(2d3k)24a2(d3k2)
Reorder the factors of 24d3k2a2.
3v(3a2)24d3a2k2-5d3u(2d3k)24a2(d3k2)
Reorder the factors of 24a2(d3k2).
3v(3a2)24d3a2k2-5d3u(2d3k)24d3a2k2
3v(3a2)24d3a2k2-5d3u(2d3k)24d3a2k2
Combine the numerators over the common denominator.
3v(3a2)-5d3u(2d3k)24d3a2k2
Simplify the numerator.
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Rewrite using the commutative property of multiplication.
3⋅3(va2)-5d3u(2d3k)24d3a2k2
Multiply 3 by 3.
9(va2)-5d3u(2d3k)24d3a2k2
Multiply d3 by d3 by adding the exponents.
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Move d3.
9va2-5(d3d3)u(2k)24d3a2k2
Use the power rule aman=am+n to combine exponents.
9va2-5d3+3u(2k)24d3a2k2
Add 3 and 3.
9va2-5d6u(2k)24d3a2k2
9va2-5d6u(2k)24d3a2k2
Multiply 2 by -5.
9va2-10d6uk24d3a2k2
9va2-10d6uk24d3a2k2
Combine (3v)/(8d^3k^2)-(5d^3u)/(12a^2k)

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