Question

Simplify the expression: (15-8)^9
—————
[ (5+2)^2]^3

Answer 1

343

Explanation:

Remember the order of operations you have to solve in, or PEMDAS, which stands for parentheses, exponents, multiplication and division (left to right, whichever one is leftmost do first), and addition and subtraction (left to right, the same as stated earlier).

1) First, simplify what it's inside the innermost parentheses:

`((15-8)^9)/([(5+2)^2]^3) \\= ((7)^9)/([(7)^2]^3) \\`

`= ((7)^9)/([7^2]^3) \\`

2) To make things easier, you don't actually have to multiply out 7 to the ninth power on the numerator yet. You can keep it there for now. Instead, just distribute the exponent of 3 that's outside the brackets to the 7 squared inside - but don't multiply everything out - only multiply the exponents, writing
`7^6`.

`= ((7)^9)/([7^2]^3) \\(7^9)/(7^6)`

3) This way, by having the same bases of 7, it is easier to solve without multiplying out huge numbers. All you have to do now is divide exponents of the same base. You only have to subtract the exponents to do this:

`(7^9)/(7^6) \\= 7^9^-^6\\= 7^3`

4) Finally, multiply
`7^3` out:

`= 7^3\\= (7) (7) (7) \\= 343`

Thus, the answer is 343.