Question

maths question of exponent ​

Answer 1

Answer:

5^4 = 25

11^2 = 121

11^4 = 14,641

5^4 = 625

5^2 = 25

4^2 = 16

25/121 × 14641/625 × 25/16

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Answer 2

Question

Simplify ⇒ $(\frac{5}{11})^{ 2} \times (\frac{11}{5})^{4} \times (\frac{5}{4})^{2}$

$\rule{300}{1}$

Answer

To find the answer we must apply laws of exponent. Here for the second number we will apply this law ⇒ $\frac{1}{a^{m}}= a^{-m}$

$(\frac{5}{11})^{ 2} \times (\frac{11}{5})^{4} \times (\frac{5}{4})^{2}$

$(\frac{5}{11})^{ 2} \times (\frac{5}{11})^{-4} \times (\frac{5}{4})^{2}$

Since we the bases are same we will apply this law of exponent next ⇒ $a^{m}\times a^{n} = a^{m+n}$

$(\frac{5}{11})^{ 2} \times (\frac{5}{11})^{-4} \times (\frac{5}{4})^{2}$

$(\frac{5}{11})^{ 2+-4} \times (\frac{5}{4})^{2}$

$(\frac{5}{11})^{ 2-4} \times (\frac{5}{4})^{2}$

$(\frac{5}{11})^{ -2} \times (\frac{5}{4})^{2}$

Now we will have to apply this law of exponent ⇒ $a^{-m} = \frac{1}{a^{m}}$

$(\frac{5}{11})^{ -2} \times (\frac{5}{4})^{2}$

$(\frac{11}{5})^{ 2} \times (\frac{5}{4})^{2}$

Since the exponents are the same we will apply this law of exponent next ⇒ $a^{m} \times b^{m} = (ab)^{m}$

$(\frac{11}{5})^{ 2} \times (\frac{5}{4})^{2}$

$(\frac{11}{5} \times \frac{5}{4})^{2}$

$(\frac{11}{4})^{2$

Since this question only tells to simplify you can either leave it here or find the actual value. I'll find the actual value for final answer here.

$(\frac{11}{4})^{2$

$\frac{11\times 11 }{4\times 4 }$

$\frac{121}{16}$

$\bf \therefore (\frac{5}{11})^{ 2} \times (\frac{11}{5})^{4} \times (\frac{5}{4})^{2} = \frac{121}{16}$

$\rule{300}{1}$