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General

General

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Question

Solve: $left parenthesis cube root of 4 right parenthesis to the power of 2 x minus 1 divided by 2 end exponent equals 1 divided by 32$

hint Hint:

In Mathematics, lets say, "a" represents a number and " " is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where is called the base and n is its power/ exponent.
$a to the power of n equals a cross times a cross times horizontal ellipsis cross times a$ n times

The correct answer is: -7/2

step by step solution :-
$left parenthesis cube root of 4 right parenthesis to the power of 2 x minus 1 divided by 2 end exponent equals 1 divided by 32$
$therefore space of 1em open parentheses cube root of left parenthesis 2 right parenthesis squared end root close parentheses to the power of 2 x minus 1 divided by 2 end exponent equals 1 divided by 2 to the power of 5$
$therefore space of 1em open parentheses 2 to the power of 2 divided by 3 end exponent close parentheses to the power of 2 x minus 1 divided by 2 end exponent equals 1 divided by 2 to the power of 5.$ $open square brackets blank to the power of m square root of open parentheses b to the power of n close parentheses end root equals b to the power of n divided by m end exponent close square brackets$
$therefore space of 1em left parenthesis 2 right parenthesis to the power of 2 divided by 3 ∗ left parenthesis 2 x minus 1 divided by 2 right parenthesis end exponent equals 1 divided by 2 to the power of 5$ $open square brackets open parentheses b to the power of n close parentheses to the power of m equals b to the power of n m end exponent close square brackets$
$therefore left parenthesis 2 right parenthesis to the power of left parenthesis 2 divided by 3 cross times 2 x right parenthesis minus left parenthesis 2 divided by 3 cross times 1 divided by 2 right parenthesis end exponent equals 1 divided by 2 to the power of 5$
$therefore space of 1em left parenthesis 2 right parenthesis to the power of left parenthesis 4 divided by 3 x right parenthesis minus left parenthesis 1 divided by 3 right parenthesis end exponent equals 1 divided by 2 to the power of 5$
$therefore space of 1em left parenthesis 2 right parenthesis to the power of left parenthesis 4 divided by 3 x minus 1 divided by 3 right parenthesis end exponent equals left parenthesis 2 right parenthesis to the power of negative 5 end exponent$ $open parentheses b to the power of negative n end exponent equals 1 divided by b to the power of n close parentheses$
$therefore left parenthesis 4 divided by 3 x minus 1 divided by 3 right parenthesis equals negative 5$ (Exponents of the same base in an equation are equal)
$therefore space of 1em left parenthesis 4 x minus 1 right parenthesis equals negative 5 cross times 3$
$therefore space left parenthesis 4 x minus 1 right parenthesis space equals negative 15 therefore 4 x space equals negative 15 plus 1 therefore 4 x space equals negative 14 right parenthesis$
$therefore space of 1em straight x equals negative 14 divided by 4$
$therefore space of 1em straight x equals negative 7 divided by 2.$ (Dividing both sides by 2)

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