Question

(√9)^3 *(√81)^5 ÷ (27)^2​

Answer 1

Answer:

2187

Step-by-step explanation:

We know

√9=3, √81=9 so,

${3}^{3} \times {9}^{5} \div {27}^{2}$

Now,

$9 = {3}^{2} and \: 27 = {3}^{3}$

so

${3}^{3} \times {( {3}^{2}) }^{5} \div {( {3}^{3} )}^{2}$

by using the formulas

${( {a}^{b}) }^{c} = {a}^{bc} \\ { a }^{m} \times {a}^{n} = {a}^{m + n} \\ {a}^{x} \div {a}^{y} = {a}^{x - y}$

we get the final result as

${3}^{3 + (2 \times 5) - (3 \times 2)} \\ = {3}^{3 + 10 - 6} = {3}^{13 - 6} \\ = {3}^{7} = {3}^{3 + 3 + 1}$

$= {3}^{3} \times {3}^{3} \times 3 \\ = 27 \times 27 \times 3 \\ = 2187$

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