Simplify and rewrite the expression so each variable only appears once.

Tobias Ali

Tobias Ali

Answered question

2021-09-13

Simplify and rewrite the expression so each variable only appears once.
a16b10(a2b3)4

Answer & Explanation

2k1enyvp

2k1enyvp

Skilled2021-09-14Added 94 answers

We can use the exponent rules,
aman=am+n
(am)n=amn
We can also use the radical to exponent conversion rules,
n{am}=amn
an=a1n
Also we can use the radical form ab=ab
Consider the expression a16b10(a2b3)4
Use the radical form ab=ab to simplify the radical term and split the exponent term.
a16b10(a2b3)4=a16b10(a2)4(b3)4
To further simplify the expression use the rules, (am)n=amn,n{am}=amn, we get
a16b10(a2)4(b3)4=a162b102a2(4)b3(4)
=a8b5a8b12
=a88b5+12
=a0b17
=1b17
=b17
Hence the simplest form of the given expression is b17

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