The correct option is B 5^5Since (a^m)^n=a^mn where a,m and n are integers (a≠ 0), we have (5^3)^4=5^12. ∵ a^m× a^n=a^m+n ∴ (5^3)^4× 5^3=5^12× 5^3=5^12+3 ...

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Byju's Answer

Standard VIII

Mathematics

Power Law

534× 53 ÷ 510...

Question

$((5^{3})^{4} \times 5^{3}) \div 5^{10}$ = ___

5^{3}

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5^{5}

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1

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5^{- 5}

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Solution

The correct option is B $5^{5}$
Since $(a^{m})^{n} = a^{m n}$ where $a, m$ and $n$ are integers ( $a \neq 0$ ), we have $(5^{3})^{4} = 5^{12} .$
$∵ a^{m} \times a^{n} = a^{m + n}$
$∴ (5^{3})^{4} \times 5^{3} = 5^{12} \times 5^{3} = 5^{12 + 3} = 5^{15}$
Thus, $((5^{3})^{4} \times 5^{3}) \div 5^{10} = \frac{5^{15}}{5^{10}}$
$∵ \frac{a^{m}}{a^{n}} = a^{m - n} = 5^{15 - 10} = 5^{5}$

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Similar questions

[{(5^{3})}^{4} \times 5^{4}] \div 5^{14}

Q. Simplify:

5 \frac{3}{4} - 4 \frac{5}{12} + 3 \frac{1}{6}

Q. Find the sum of

273

and

534

Q. The value of

{c o s e c}^{2} 51^{0} - {c o t}^{2} 51^{0}

Fill in the blank

\begin{matrix} 213 & (180) & 534 352 & (-) & 612 \end{matrix}

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((53)4×53)÷510 = ___

The correct option is B 55Since (am)n=amn where a,m and n are integers (a≠0), we have (53)4=512. ∵am×an=am+n ∴(53)4×53=512×53=512+3 =515 Thus, ((53)4×53)÷510=515510 ∵aman=am−n=515−10=55

$((5^{3})^{4} \times 5^{3}) \div 5^{10}$ = ___