Question

simplify and express each of the following in exponential form

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Answer 1

$\huge \boxed{ \blue{ {7}^{8} \times {13}^{3} }}$

Step-by-step explanation:

$\dfrac{ {3}^{2} \times {7}^{13} \times {13}^{6} }{ {21}^{2} \times {91}^{3} } \\ \\ = > \frac{ {3}^{2} \times {7}^{13} \times {13}^{6} }{ {(3 \times 7)}^{2} \times {(7 \times 13)}^{3} } \\ \\ = > \frac{ {3}^{2} \times {7}^{13} \times {13}^{6} }{ {3}^{2} \times {7}^{2} \times {7}^{3} \times {13}^{3} } \\ \\ = > \frac{ {3}^{2} \times {7}^{13} \times {13}^{6} }{ {3}^{2} \times {7}^{2 + 3} \times {13}^{3} } \\ \\ = > \frac{ {3}^{2} \times {7}^{13} \times {13}^{6} }{ {3}^{2} \times {7}^{5} \times {13}^{3} } \\ \\ = > {3}^{2 - 2} \times {7}^{13 - 5} \times {13}^{6 - 3} \\ \\ = > {3}^{0} \times {7}^{8} \times {13}^{3} \\ \\ = > 1 \times {7}^{8} \times {13}^{3} \\ \\ = > \underline \red{ {7}^{8} \times {13}^{3} }$

So the answer is 7⁸ × 13³.

Property used -

Properties about exponents,

when bases are same (here x) -

${x}^{m} \times {x}^{n} = {x}^{m + n} \\ {x}^{m} \div {x}^{n} = {x}^{m - n} \\ {(x}^{m} {)}^{n} = {x}^{m \times n}$

when exponents are same,

${x}^{ m} \times {y}^{m} = (x \times y) {}^{m}$

Answer 2

➤ Answer

• $\bf{\green{{7}^{8} \times {13}^{3}}}$

➤ To Find

• The value of $\cfrac{ {3}^{2} \times{7}^{13} \times{13}^{6}}{ {21}^{2} \times {91}^{3} }$

➤ Step By Step Explanation

In this question we need to find the value of $\cfrac{ {3}^{2} \times{7}^{13} \times{13}^{6}}{ {21}^{2} \times {91}^{3} }$.

We can easily find the value by using laws of exponents. So let's do it !!

➠ Formula Used

$\dag \boxed{ \tt{x}^{m} \times {x}^{n} = {x}^{m + n}} \\ \\ \dag \boxed{ \tt \cfrac{ {x}^{m} }{ {x}^{n} } = {x}^{m - n}} \\ \\ \dag \boxed{\tt {x}^{m} \times {y}^{m} = {(xy)}^{m}}\\ \\ \dag\boxed {\tt {x}^{0} = 1}$

➠ Solution

$\longmapsto\tt\cfrac{ {3}^{2} \times{7}^{13} \times{13}^{6}}{ {21}^{2} \times {91}^{3} } \\ \\\longmapsto\tt \cfrac{ {3}^{2} \times{7}^{13} \times{13}^{6}}{ {(3 \times 7)}^{2} \times {(7 \times 13)}^{3} } \\ \\\longmapsto\tt \cfrac{ {3}^{2} \times{7}^{13} \times{13}^{6}}{ {3}^{2} \times {7}^{2} \times {7}^{3} \times {13}^{3} } \\ \\\longmapsto\tt \cfrac{ {3}^{2} \times{7}^{13} \times{13}^{6}}{ {3}^{2} \times {7}^{2 + 3} \times {13}^{3} } \\ \\\longmapsto\tt \cfrac{ {3}^{2} \times{7}^{13} \times{13}^{6}}{ {3}^{2} \times {7}^{5} \times {13}^{3} } \\ \\ \longmapsto\tt{3}^{2 - 2} \times {7}^{13 - 5} \times {13}^{6 - 3} \\ \\ \longmapsto\tt {3}^{0} \times {7}^{8} \times {13}^{3} \\ \\\longmapsto\tt 1 \times {7}^{8} \times {13}^{3} \\ \\\longmapsto\bf{\green{ {7}^{8} \times {13}^{3}}}$

➵ Therefore, answer = ${7}^{8} \times {13}^{3}$

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