Question 85 d Evaluate 34- 123- 36-25- 63

We have 3^4 × 12^3 × 36/2^5 × 6^3 = 3^4 × (2^2 × 3)^3 × 6^2/2^5 × 6^3 = 3^4 × 2^6 × 3^3 × 6^2/2^5 × 6^3 = 3^9 × 2^6 × 6^2/2^5 × 6^3 = 3^9 × 2^6 5× 6^2 3 ...

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Standard VII

Mathematics

Comparision of Quantities Using Exponents

Question 85 d...

Question

Question 85 (d)

Evaluate
$\frac{3^{4} \times 12^{3} \times 36}{2^{5} \times 6^{3}}$

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Solution

We have
$\frac{3^{4} \times 12^{3} \times 36}{2^{5} \times 6^{3}} = \frac{3^{4} \times (2^{2} \times 3)^{3} \times 6^{2}}{2^{5} \times 6^{3}} = \frac{3^{4} \times 2^{6} \times 3^{3} \times 6^{2}}{2^{5} \times 6^{3}} = \frac{3^{9} \times 2^{6} \times 6^{2}}{2^{5} \times 6^{3}} = 3^{9} \times 2^{6 - 5} \times 6^{2 - 3} = \frac{3^{9} \times 2}{2 \times 3} = 3^{8} = 6561$

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Question 85 (g)

Evaluate
$\frac{6^{4} \times 9^{2} \times 25^{3}}{3^{2} \times 4^{2} \times 15^{6}}$

Question 85 (f)

Evaluate
$\frac{15^{4} \times 18^{3}}{3^{3} \times 5^{2} \times 12^{2}}$

Q. The given below input rearranges step-by-step in particular order according to a set of rules. In this case the last step of arranged input is Step V.
Input : 85 16 36 04 19 97 63 09
Step I : 97 85 16 36 04 19 63 09
Step II : 97 85 63 16 36 04 19 09
Step III : 97 85 63 36 16 04 19 09
Step IV : 97 85 63 36 19 16 04 09
Step V : 97 85 63 36 19 16 09 04
Study the above arrangement carefully and then answer the following question.
Which of the following will be step III for their input below?
Input : 09 25 16 30 32 18 17 06

Q. Evaluate:

34 \times 36

Q. An electronic device when fed with the numbers, rearranges them in a particular order following certain rules. The following is a step-by-step process of rearrangement for the given input of numbers.
Input :- 85 16 36 04 19 97 63 09
Step I :- 97 85 16 36 04 19 63 09
Step II :- 97 85 63 16 36 04 19 09
Step III :- 97 85 63 36 16 04 19 09
Step IV :- 97 85 63 36 19 16 04 09
Step V :- 97 85 63 36 19 16 09 04
(for the given input step V is the last step).
Which of the following will be the last step for the given input?
Input :- 03 31 43 22 11 09

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Comparision of Quantities Using Exponents

Standard VII Mathematics

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Question 85 (d) Evaluate 34×123×3625×63

We have 34×123×3625×63=34×(22×3)3×6225×63=34×26×33×6225×63=39×26×6225×63=39×26−5×62−3=39×22×3=38=6561

Question 85 (d)

Evaluate
$\frac{3^{4} \times 12^{3} \times 36}{2^{5} \times 6^{3}}$