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[(53^(2)-45^(2)):7+3*2^(4)]:[(21^(2)-7*8):7-17*3]^(2)+2*5^(2)}^(2):(2^(2)+2^(3)+2^(4)+2^(5))+10*2^(2)

$\left.\left[\left(53^{2}-45^{2}\right): 7+3 \cdot 2^{4}\right]:\left[\left(21^{2}-7 \cdot 8\right): 7-17 \cdot 3\right]^{2}+2 \cdot 5^{2}\right\}^{2}:\left(2^{2}+2^{3}+2^{4}+2^{5}\right)+10 \cdot 2^{2}$

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Operations with rational exponents

Full solution

Q.

\left.\left[\left(53^{2}-45^{2}\right): 7+3 \cdot 2^{4}\right]:\left[\left(21^{2}-7 \cdot 8\right): 7-17 \cdot 3\right]^{2}+2 \cdot 5^{2}\right\}^{2}:\left(2^{2}+2^{3}+2^{4}+2^{5}\right)+10 \cdot 2^{2}

Calculate Squares and Differences: Calculate the squares and differences in the numerator and denominator. $\newline$ $53^2 - 45^2 = 2809 - 2025 = 784$ ; $21^2 - 7 \times 8 = 441 - 56 = 385$ .
Simplify Parts of Expression: Simplify each part of the expression. $\newline$ $(784/7 + 3\cdot2^4) = 112 + 3\cdot16 = 112 + 48 = 160$ ; $(385/7 - 17\cdot3) = 55 - 51 = 4$ .
Calculate Power and Division: Calculate the power and division in the denominator. $\newline$ $4^2 = 16$ ; $2^2 + 2^3 + 2^4 + 2^5 = 4 + 8 + 16 + 32 = 60$ .
Continue Simplifying Expression: Continue simplifying the main expression. $160/16 = 10$ ; $2\times5^2 = 2\times25 = 50$ .
Final Calculations: Final calculations for the expression. $\newline$ $10:60 + 50 + 10\times2^2 = \frac{10}{60} + 50 + 10\times4 = 0.1667 + 50 + 40 = 90.1667$ .

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