The Sum of degrees of polynomials y3 + 7y
4 – 6 & 3x5
(5 + x ) is ______________.
Answers
Step-by-step explanation:
Question :- Evaluate
\bf \: {(\dfrac{1}{3}) }^{ - 2} - {(\dfrac{1}{4}) }^{ - 2} + {(\dfrac{1}{5}) }^{ - 2} - {(\dfrac{1}{6}) }^{ - 2} + {(\dfrac{1}{7}) }^{ - 2}(
3
1
)
−2
−(
4
1
)
−2
+(
5
1
)
−2
−(
6
1
)
−2
+(
7
1
)
−2
Answer
Property used :
\bf \:{(\dfrac{x}{y}) }^{ - m} = {(\dfrac{y}{x}) }^{m}(
y
x
)
−m
=(
x
y
)
m
Solution :-
\bf \: {(\dfrac{1}{3}) }^{ - 2} - {(\dfrac{1}{4}) }^{ - 2} + {(\dfrac{1}{5}) }^{ - 2} - {(\dfrac{1}{6}) }^{ - 2} + {(\dfrac{1}{7}) }^{ - 2}(
3
1
)
−2
−(
4
1
)
−2
+(
5
1
)
−2
−(
6
1
)
−2
+(
7
1
)
−2
\bf\implies \: {3}^{2} - {4}^{2} + {5}^{2} - {6}^{2} + {7}^{2}⟹3
2
−4
2
+5
2
−6
2
+7
2
\bf\implies \:9 - 16 + 25 - 36 + 49⟹9−16+25−36+49
\bf\implies \:9 + 9 + 13⟹9+9+13
\bf\implies \:31⟹31
_________________________________________
Additional Information
\bf \: {x}^{m} \times {x}^{n} = {x}^{m + n}x
m
×x
n
=x
m+n
\bf \: {x}^{m} \div {x}^{n} = {x}^{m - n}x
m
÷x
n
=x
m−n
\bf \: {x}^{0} = 1x
0
=1
\bf \: {x}^{m} \times {y}^{m} = {(xy)}^{m }x
m
×y
m
=(xy)
m
___________________________________________