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क)
(5^(4)×8×16)/(2^(5)×125)

क) $\frac{5^{4} \times 8 \times 16}{2^{5} \times 125}$

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Powers with negative bases

Full solution

Q. क)

\frac{5^{4} \times 8 \times 16}{2^{5} \times 125}

Simplify Exponents: Simplify the numerator and the denominator separately. $\newline$ First, we simplify $5^4$ and $2^5$ . $\newline$ $5^4 = 5 \times 5 \times 5 \times 5 = 625$ $\newline$ $2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$
Multiply Numerator: Simplify the multiplication in the numerator. $\newline$ The numerator is $5^4 \times 8 \times 16$ . $\newline$ We already found $5^4 = 625$ , so we multiply $625$ by $8$ and then by $16$ . $\newline$ $625 \times 8 = 5000$ $\newline$ $5000 \times 16 = 80000$
Multiply Denominator: Simplify the multiplication in the denominator. $\newline$ The denominator is $2^5 \times 125$ . $\newline$ We already found $2^5 = 32$ , so we multiply $32$ by $125$ . $\newline$ $32 \times 125 = 4000$
Divide Numerator: Divide the simplified numerator by the simplified denominator. $\newline$ Now we divide the numerator $80000$ by the denominator $4000$ . $\newline$ $80000 / 4000 = 20$

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