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Elenna [48]
3 years ago
5

Which is the simplified form of the expression ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript nega

tive 3 Baseline times ((2 Superscript negative 3 Baseline) (3 squared)) squared?
Mathematics
1 answer:
ValentinkaMS [17]3 years ago
4 0

Answer:

\dfrac{1}{6561}

Step-by-step explanation:

Given the expression [(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}, Using the laws of indices to simplify the expression. The following laws will be applicable;

a^m*a^n = a^{m+n}\\(a^m)^n = a^{mn}\\

a^{-m} = 1/a^m

Given [(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}

open the parenthesis

= (2^{-2})^{-3}(3^{4})^{-3}* (2^{-3})^2(3^2)^2\\\\= 2^{-2*-3}* 3^{4*-3} * 2^{-3*2} * 3^{2*2}\\\\= 2^6 * 3^{-12} * 2^{-6} * 3^4\\\\collecting \ like \ terms\\\\= 2^6 * 2^{-6} * 3^{-12} * 3^4\\\\= 2^{6-6} * 3^{-12+4}\\\\= 2^0 * 3^{-8}\\\\= 1 * \frac{1}{3^8}\\ \\= \frac{1}{6561}

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