For the expression y5y3−(y−2)4 the correct value is in the first tile, and for the expression (y−2)4+y3y5 the correct value is in the fifth tile.
What is integer exponent?
Exponents that should be integers are known as integer exponents in mathematics. It could be either a positive or negative integer. The positive integer exponents specify how many times the base number should be multiplied by itself in this case.
We have:
[tex]=\rm y^5y^3-(y^{-2})^4[/tex]
[tex]= \rm y^{5+3}-(y^{-2\times4})[/tex]
[tex]= \rm y^{8}-(y^{-8})[/tex]
[tex]= \rm y^{8}-\dfrac{1}{y^{8}}[/tex]
[tex]\rm y^5y^3-(y^{-2})^4 = y^{8}-\dfrac{1}{y^{8}}[/tex]
Similarly,
[tex]\rm (y^{-2})^4 + \dfrac{y^3}{y^{5}} = \rm \dfrac{1}{y^{8}} + \dfrac{1}{y^{2}}[/tex]
Thus, for the expression y5y3−(y−2)4 the correct value is in the first tile, and for the expression (y−2)4+y3y5 the correct value is in the fifth tile.
Learn more about the integer exponent here:
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