(1/4^)-2×(1/2)^-3×(8^4)
Answers
Step-by-step explanation:
(
4
1
)
−2
−3(8)
3
2
(4)
0
+(
16
9
)
2
−1
=
3
16
Step-by-step explanation:
Given : Expression ( \frac{1}{4})^{ - 2}- 3(8)^{ \frac{2}{3}}(4)^{0} +( \frac{9}{16})^{ \frac{-1}{2}}(
4
1
)
−2
−3(8)
3
2
(4)
0
+(
16
9
)
2
−1
To find : Simplify the expression ?
Solution :
Expression ( \frac{1}{4})^{ - 2}- 3(8)^{ \frac{2}{3}}(4)^{0} +( \frac{9}{16})^{ \frac{-1}{2}}(
4
1
)
−2
−3(8)
3
2
(4)
0
+(
16
9
)
2
−1
Factor the bracket terms into power,
={4}^{2} - 3( {2}^{3} ) {}^{ \frac{2}{3} } \times 1 + ( \frac{3}{4} ) {}^{2 \times ( \frac{ - 1}{2}) }=4
2
−3(2
3
)
3
2
×1+(
4
3
)
2×(
2
−1
)
=16 - 3 \times {2}^{2} + ( \frac{3}{4} ) {}^{ - 1}=16−3×2
2
+( 4
3 )
−1
=16 - 12 + \frac{4}{3}=16−12+
3
4
=4 + \frac{4}{3}=4+
3
4
=\frac{12 + 4}{3}=
3
12+4
=\frac{16}{3}=
3
16
Therefore, ( \frac{1}{4})^{ - 2}- 3(8)^{ \frac{2}{3}}(4)^{0} +( \frac{9}{16})^{ \frac{-1}{2}}=\frac{16}{3}(
4
1
)
−2
−3(8)
3
2
(4)
0
+(
16
9
)
2
−1
=
3
16
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[{(-1/4)^2}^-1]^-2 simplify
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