Question

Simplify
(1/4)^-2 - 3(8)^2/3 (4)^0 + (9/16)^-1/2

Answer 1

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Here is your answer.

$( \frac{1}{4}) {}^{ - 2} - 3(8) {}^{ \frac{2}{3} } (4) {}^{0} + ( \frac{9}{16} ) {}^{ \frac{ - 1}{2} } \\ \\ = {4}^{2} - 3( {2}^{3} ) {}^{ \frac{2}{3} } \times 1 + ( \frac{3}{4} ) {}^{2 \times ( \frac{ - 1}{2}) } \\ \\ = 16 - 3 \times {2}^{2} + ( \frac{3}{4} ) {}^{ - 1} \\ \\ = 16 - 12 + \frac{4}{3} \\ \\ = 4 + \frac{4}{3} \\ \\ = \frac{12 + 4}{3} \\ \\ = \frac{16}{3}$
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Answer 2

$( \frac{1}{4})^{ - 2}- 3(8)^{ \frac{2}{3}}(4)^{0} +( \frac{9}{16})^{ \frac{-1}{2}}=\frac{16}{3}$

Step-by-step explanation:

Given : Expression $( \frac{1}{4})^{ - 2}- 3(8)^{ \frac{2}{3}}(4)^{0} +( \frac{9}{16})^{ \frac{-1}{2}}$

To find : Simplify the expression ?

Solution :

Expression $( \frac{1}{4})^{ - 2}- 3(8)^{ \frac{2}{3}}(4)^{0} +( \frac{9}{16})^{ \frac{-1}{2}}$

Factor the bracket terms into power,

$={4}^{2} - 3( {2}^{3} ) {}^{ \frac{2}{3} } \times 1 + ( \frac{3}{4} ) {}^{2 \times ( \frac{ - 1}{2}) }$

$=16 - 3 \times {2}^{2} + ( \frac{3}{4} ) {}^{ - 1}$

$=16 - 12 + \frac{4}{3}$

$=4 + \frac{4}{3}$

$=\frac{12 + 4}{3}$

$=\frac{16}{3}$

Therefore,  $( \frac{1}{4})^{ - 2}- 3(8)^{ \frac{2}{3}}(4)^{0} +( \frac{9}{16})^{ \frac{-1}{2}}=\frac{16}{3}$

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