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${:8^(5)÷8^(3))×8^(-2)$

$\left.8^{5} \div 8^{3}\right) \times 8^{-2}$

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Evaluate integers raised to rational exponents

Full solution

Q.

\left.8^{5} \div 8^{3}\right) \times 8^{-2}

Apply Quotient Rule: Use the quotient rule for exponents: $a^{m}/a^{n} = a^{(m-n)}$ . $\newline$ Calculate $8^{5}\div8^{3}$ . $\newline$ $8^{(5-3)} = 8^2$
Calculate $8^{5}\div8^{3}$ : Now multiply $8^2$ by $8^{-2}$ using the product rule for exponents: $a^{m} \times a^{n} = a^{m+n}$ . $\newline$ Calculate $8^2 \times 8^{-2}$ . $\newline$ $8^{2 + (-2)} = 8^0$
Apply Product Rule: Recognize that any non-zero number raised to the power of $0$ is $1$ . $\newline$ Calculate $8^0$ . $\newline$ $8^0 = 1$

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