Simplify `7^2+7 +7^-1-root(3)(27)```

Please show your steps clearly.Thanks

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`7^2+7+7^(-1)-root(3)(27)`

To simplify, apply the order of operations PEMDAS.

Note that exponent comes before addition and subtraction in PEMDAS, then we do the exponent first.

Since

`7^2=7*7=49` ,

`7^(-1)=1/7^1=1/7` and

`root(3)(27)=root(3)(3^3)=3` ,

the expression becomes:

`=49+7+1/7^1 - 3`

`=49 + 7+1/7-3`

Now that the remaining operations are addition and subtraction, we need to express the whole number as fractions.

`=49/1+7/1+1/7-3/1`

Then, express them with same denominator.

Since the LCD is 7, multiply 49/1, 7/1 and 3/1 by 7/7.

`=49/1*7/7+7/1*7/7+1/7-3/1*7/7`

`=343/7+49/7+1/7-21/7`

Then, simplify starting from the left. So, add the first three fractions.

`=393/7-21/7`

And, subtract.

`=372/7`

`=53 1/7`

**Hence, `7^2+7+7^(-1)-root(3)(27)=53 1/7` .**

Your question can be solved with application of BODMAS rule

`7^2+7+7^(-1)-root3(27)`

`49+7+7^(-1)-(27)^(1/3)`

`49+7+7^(-1)-(3^3)^(1/3)`

`49+7+1/7-3^(3xx(1/3))`

`49+7+1/7-3`

`56+1/7-3`

`56-3+1/7`

`53+1/7`

`(53xx7)/7+1/7`

`371/7+1/7`

`(371+1)/7`

`372/7`

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