Find the value of (216) raised to 2/3 + (256) raised to 3/4
Answers
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216
−
3
2
4
+
256
4
3
1
+
243
−
5
1
2
=214
Solution:
As we can the power in the denominator are in negative the value of the power will change if brought in with numerator.
Given: \frac{4}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{2}{243^{-\frac{2}{5}}}
216
−
3
2
4
+
256
−
4
3
1
+
243
−
5
2
2
Changing the power in decimal for easier multiplication or can be left in fraction form also as below,
4 \times(216)^{0.66}+1 \times(256)^{0.75}+2 \times(243)^{0.2}4×(216)
0.66
+1×(256)
0.75
+2×(243)
0.2
The values of 216, 256 and 243 are to be changed into their lowest form along with perfect power as we can see the numbers 216, 256 and 243 are changed into forms of 6, 4 and 3.
4 \times(6^{3})^{0.66}+1 \times(4^{4})^{0.75}+2 \times(3^{5})^{0.2}4×(6
3
)
0.66
+1×(4
4
)
0.75
+2×(3
5
)
0.2
Simplifying the values and then adding the numbers we get:
144 + 64 + 6 = 214