Math

QuestionEvaluate (x2n2)(xn+3)(x2n1)\frac{\left(x^{2 n-2}\right)\left(x^{n+3}\right)}{\left(x^{2 n-1}\right)} for x=2x=2 and n=3n=-3.

Studdy Solution

STEP 1

Assumptions1. The given expression is (xn)(xn+3)(xn1)\frac{\left(x^{ n-}\right)\left(x^{n+3}\right)}{\left(x^{ n-1}\right)} . The given values are x=x= and n=3n=-3

STEP 2

First, we need to substitute the given values of xx and nn into the expression.
(22()2)(2+)(22()1)\frac{\left(2^{2 (-)-2}\right)\left(2^{-+}\right)}{\left(2^{2 (-)-1}\right)}

STEP 3

Next, we simplify the exponents in the expression.
(262)(20)(261)\frac{\left(2^{-6-2}\right)\left(2^{0}\right)}{\left(2^{-6-1}\right)}

STEP 4

Further simplify the exponents.
(28)(20)(27)\frac{\left(2^{-8}\right)\left(2^{0}\right)}{\left(2^{-7}\right)}

STEP 5

Now, we simplify the expression. Remember that any number raised to the power of0 is1, and a negative exponent means that the base is on the denominator of a fraction.
1281127\frac{\frac{1}{2^{8}} \cdot1}{\frac{1}{2^{7}}}

STEP 6

implify the expression further by multiplying the numerator and denominator by 282^{8} to remove the fraction in the numerator.
128\frac{1}{2^{8-}}

STEP 7

implify the exponent in the denominator.
121\frac{1}{2^{1}}

STEP 8

Finally, simplify the expression to find the result.
12\frac{1}{2}So, the value of the expression for x=2x=2 and n=3n=-3 is 12\frac{1}{2}.

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