Question

plz give with explanation pic​

Answer 1

Answer:

108

Step-by-step explanation:

Hope it is helpful to you!!!

Answer 2

Given to find the value of :-

$\dfrac{(27) {}^{3} \times (16) {}^{2} \times (15) {}^{2} }{9 {}^{4} \times (5) {}^{2} \times 2 {}^{6} }$

Answer :-

108

Solution :-

Let's simplify this question by using some exponent and laws

=> Let's write the bases in simplest form

$\begin{gathered}\begin{array}{c | c} \underline3 &\underline{27} \\ \underline3&\underline{9} \\ \underline3 &\underline{3}\\ &1\end{array}\end{gathered}$

27 can be written as 3³

$\begin{gathered}\begin{array}{c | c} \underline2 &\underline{16} \\ \underline2&\underline{8} \\ \underline2 &\underline{4}\\ \underline2&\underline{2} \\ &\underline{1}\\ &\end{array}\end{gathered}$

16 can be written as 2⁴

15 can be written as 3 × 5

So, Let's substitute them

$\dfrac{(27) {}^{3} \times (16) {}^{2} \times (15) {}^{2} }{9 {}^{4} \times (5) {}^{2} \times 2 {}^{6} }$

$\dfrac{(3 {}^{3} ) {}^{3} \times (2 {}^{4} ) {}^{2} \times (3 \times 5) {}^{2} }{(3 {}^{2} ) {}^{4} \times (5) {}^{2} \times 2 {}^{6} }$

We know that,

$\red {(a {}^{m} ) {}^{n} = a {}^{mn} }$

$\red{(a \times b) {}^{2} = a {}^{2}b {}^{2} }$

So, this gives

$\dfrac{(3 {}^{9} ) \times (2 {}^{8} ) \times (3 ) {}^{2} \times (5) {}^{2} }{(3 {}^{8} ) \times (5) {}^{2} \times 2 {}^{6} }$

$\dfrac{(3 {}^{9} ) \times (3 ) {}^{2} \times (2 {}^{8} ) (5) {}^{2} }{(3 {}^{8} ) \times (5) {}^{2} \times 2 {}^{6} }$

As also we know that,

$\red{a {}^{m} \times a {}^{n} = a {}^{m + n} }$

$\dfrac{(3 {}^{9 + 2} ) \times (2 {}^{8} ) \times (5) {}^{2} }{(3 {}^{8} ) \times (5) {}^{2} \times 2 {}^{6} }$

$\dfrac{(3 {}^{11} ) \times (2 {}^{8} ) \times (5) {}^{2} }{(3 {}^{8} ) \times (5) {}^{2} \times 2 {}^{6} }$

Tranposing all denominator terms to numerator

${(3 {}^{11} ) \times (2 {}^{8} ) \times (5) {}^{2} \times }{(3 {}^{ - 8} )} \times 5 {}^{ - 2} \times 2 {}^{ - 6}$

Keeping like terms together

$3 {}^{11} \times 3 {}^{ - 8} \times 2 {}^{8} \times 2 {}^{ - 6} \times 5 {}^{2} \times 5 {}^{ - 2}$

Again applying this formula

$\red{a {}^{m} \times a {}^{n} = a {}^{m + n} }$

This gives,

$3 {}^{3} \times 2 {}^{2}$

$3 \times 3 \times 3 \times 2 \times 2$

$27 \times 4$

$108$

So, the required answer is 108

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