Answer:
1.
[tex] {(625)}^{ \frac{ - 1}{4} } = ({(5)}^{4})^{ \frac{ - 1}{4} } \: \: \: \: (5 \: to \: the \: power \: 4 \: is \: 625 ) \\ = {5}^{4 \times \frac{ (- 1)}{4} } = {5}^{ - 1} = \frac{1}{5^{1} } = \frac{1}{5} = 0.2[/tex]
2.
[tex] {a}^{m} + {a}^{n} = {a}^{m + n} \\ \\ this \: is \: known \: as \: product \: law \: of \: exponent \: [/tex]
We can apply it only when the base is same
3.
[tex] \frac{x^{m} }{x^{n} } = {x}^{m - n \: } \\ \\ this \: is \: quotient \: law \: of \: exponent \: \\[/tex]
We can apply it only when numeator and denominator are same
4.
[tex]( {(a)}^{m})^{n} = {a}^{mn} \\ \\ this \: is \: known \: as \: power \: law \: of \: exponent \: [/tex]
and answer to fifth question is given in above attachment. we answer 5th question using law of exponent.
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Verified answer
Answer:
1.
[tex] {(625)}^{ \frac{ - 1}{4} } = ({(5)}^{4})^{ \frac{ - 1}{4} } \: \: \: \: (5 \: to \: the \: power \: 4 \: is \: 625 ) \\ = {5}^{4 \times \frac{ (- 1)}{4} } = {5}^{ - 1} = \frac{1}{5^{1} } = \frac{1}{5} = 0.2[/tex]
2.
[tex] {a}^{m} + {a}^{n} = {a}^{m + n} \\ \\ this \: is \: known \: as \: product \: law \: of \: exponent \: [/tex]
We can apply it only when the base is same
3.
[tex] \frac{x^{m} }{x^{n} } = {x}^{m - n \: } \\ \\ this \: is \: quotient \: law \: of \: exponent \: \\[/tex]
We can apply it only when numeator and denominator are same
4.
[tex]( {(a)}^{m})^{n} = {a}^{mn} \\ \\ this \: is \: known \: as \: power \: law \: of \: exponent \: [/tex]
and answer to fifth question is given in above attachment. we answer 5th question using law of exponent.
HOPE IT HELPS YOU :)
IF YES THEN PLEASE PLEASE MARK AS BRANIEST AND FOLLOW TOO :)