How do you use the laws of exponents to simplify the expression #b^8(2b)^7#?

1 Answer
smendyka
Jun 30, 2018

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the term within the parenthesis:

#a = a^color(red)(1)#

#b^8(2b)^7 => b^8(2^color(red)(1)b^color(red)(1))^7#

Now, use this rule of exponents to eliminate the need for parenthesis:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#b^8(2^color(red)(1)b^color(red)(1))^color(blue)(7) => b^8 2^(color(red)(1) xx color(blue)(7))b^(color(red)(1) xx color(blue)(7)) => b^8 2^7b^7 => b^8 128b^7#

Now, rewrite the expression and use this rule of exponents to complete the simplification:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#b^8 128b^7 => 128b^color(red)(8) xx b^color(blue)(7) => 128b^(color(red)(8)+color(blue)(7)) => 128b^15#

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