Simplify each expression. Write answers without negative exponents. Assume all v

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Answered question

2021-10-12

Condense each expression. Answers should not contain negative exponents. Assume that every variable is a positive real number.
(121100)32

Answer & Explanation

davonliefI

davonliefI

Skilled2021-10-13Added 79 answers

So we need, consider the expression (121100)32 and use the exponent property (ab)m=(ba)m to simplify this expression.
(121100)32=(100121)32
Since 100 and 121 can be written as 102 and 112,100121=102112.
Then we use the property ambm=(ab)m to simplify the expression further.
(100121)32=(102112)32
=[(1011)2]32
And now, apply the exponent rules [(ab)m]n=(ab)mn and ambm=(ab)m to simplify the expression further.
[(1011)2]32=(1011)2×32
=(1011)3
=103113
Since 10=2×5,103113=(2×5)3113. Now, use the exponent rule (ab)m=ambm to simplify it further.
103113=(2×5)3113
=2353113
Hence, (121100)32=2353113

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