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

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Answered question

2021-10-24

Simplify each expression. Write answers without negative exponents. Assume all variables represent nonzero real numbers.
(5x)2(5x3)3(52x3)3

Answer & Explanation

Bentley Leach

Bentley Leach

Skilled2021-10-25Added 109 answers

Given expression: (5x)2(5x3)3(52x3)3 
Apply the power-base rule: (xy)a=xaya 
Then it can be written as follows: 
(5x)2(5x3)3(52x3)3=(52)(x2)(5)3(x3)3(52)3(x3)3 
Use the power rule for exponents: (xa)b=xab then write separately numerical and variable factors. 
(5x)2(5x3)3(52x3)3=(5)2(x)2(5)3(x)9(5)6(x)9 
=(5)2(5)3(x)2(5)6 
Use the product rule for exponents: (xa)(xb)=xa+b 
(5)2(5)3(x)2(5)6=(5)23(x)2(5)6 
=(5)5(x)2(5)6 
Use the quotient rule for exponents: xaxb=xab 
(5)5(x)2(5)6(5)5+6(x)2 
 

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