Simplify ((s^(2+t^3))^4*((s^2)/(t^3))^3)÷((s/t)^5)

Math
(s2+t3)4⋅(s2t3)3÷(st)5
Rewrite the division as a fraction.
(s2+t3)4⋅(s2t3)3(st)5
Simplify the numerator.
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Apply the product rule to s2t3.
(s2+t3)4(s2)3(t3)3(st)5
Multiply the exponents in (s2+t3)4.
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Apply the power rule and multiply exponents, (am)n=amn.
s(2+t3)⋅4(s2)3(t3)3(st)5
Apply the distributive property.
s2⋅4+t3⋅4(s2)3(t3)3(st)5
Multiply 2 by 4.
s8+t3⋅4(s2)3(t3)3(st)5
Move 4 to the left of t3.
s8+4t3(s2)3(t3)3(st)5
s8+4t3(s2)3(t3)3(st)5
Multiply the exponents in (s2)3.
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Apply the power rule and multiply exponents, (am)n=amn.
s8+4t3s2⋅3(t3)3(st)5
Multiply 2 by 3.
s8+4t3s6(t3)3(st)5
s8+4t3s6(t3)3(st)5
Multiply the exponents in (t3)3.
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Apply the power rule and multiply exponents, (am)n=amn.
s8+4t3s6t3⋅3(st)5
Multiply 3 by 3.
s8+4t3s6t9(st)5
s8+4t3s6t9(st)5
s8+4t3s6t9(st)5
Combine fractions.
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Apply the product rule to st.
s8+4t3s6t9s5t5
Combine s8+4t3 and s6t9.
s8+4t3s6t9s5t5
s8+4t3s6t9s5t5
Multiply s8+4t3 by s6 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
s8+4t3+6t9s5t5
Add 8 and 6.
s4t3+14t9s5t5
s4t3+14t9s5t5
Multiply the numerator by the reciprocal of the denominator.
s4t3+14t9⋅t5s5
Cancel the common factor of t5.
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Factor t5 out of t9.
s4t3+14t5t4⋅t5s5
Cancel the common factor.
s4t3+14t5t4⋅t5s5
Rewrite the expression.
s4t3+14t4⋅1s5
s4t3+14t4⋅1s5
Multiply s4t3+14t4 and 1s5.
s4t3+14t4s5
Cancel the common factor of s4t3+14 and s5.
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Factor s5 out of s4t3+14.
s5s4t3+9t4s5
Cancel the common factors.
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Factor s5 out of t4s5.
s5s4t3+9s5t4
Cancel the common factor.
s5s4t3+9s5t4
Rewrite the expression.
s4t3+9t4
s4t3+9t4
s4t3+9t4
Simplify ((s^(2+t^3))^4*((s^2)/(t^3))^3)÷((s/t)^5)

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