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Simplify the following term and fetch the result
$\dfrac{{{{\left( {{2^5}} \right)}^2} \times {7^3}}}{{{8^3} \times 7}}$

seo-qna
Last updated date: 28th May 2024
Total views: 439.8k
Views today: 12.39k
Answer
VerifiedVerified
439.8k+ views
Hint: Solve by using algebraic formulas, not by vigorous calculation.

Given:$\dfrac{{{{\left( {{2^5}} \right)}^2} \times {7^3}}}{{{8^3} \times 7}}$
We know that$\left[ {{{\left( {{x^a}} \right)}^b} = {x^{a \times b}}\& \left( {{2^3}} \right) = 8} \right]$
So continuing further
$
\dfrac{{{{\left( {{2^5}} \right)}^2} \times {7^3}}}{{{8^3} \times 7}} \\
= \dfrac{{{{\left( {{2^5}} \right)}^2} \times {7^3}}}{{{{\left( {{2^3}} \right)}^3} \times 7}} \\
= \dfrac{{\left( {{2^{5 \times 2}}} \right) \times {7^3}}}{{\left( {{2^{3 \times 3}}} \right) \times 7}}
\\
= \dfrac{{{2^{10}} \times {7^3}}}{{{2^9} \times 7}} \\
= 2 \times {7^2} = 2 \times 49 = 98 \\
$
Hence, 98 is the solution.

Note:In such a type of problem which contains lots of numerical values, never try to simplify the terms by doing large calculations as that will be very tedious. Try to solve by cancelling some terms and then proceeding further.