Question

Simplify and write in exponential form with positive exponent:​

Answer 1

Answer:

Step-by-step explanation:

(4/49) x ( 8 / 343) ÷ (7/5) ^8

= (2^5 / 7^5 )x 5^8 / 7^8

= 2^5 x 5^8 / 7^ 13

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Answer 2

Answer:

$\boxed{\red{\sf \bigg(\dfrac{2}{7}\bigg)^2 \times \bigg(\dfrac{7}{2}\bigg)^{-3} \div \left\{ \left( \dfrac{7}{5}\right)^{-2}\right\}^{-4} =\dfrac{ 2^5\times 5^8}{7^{13}} }}$

Step-by-step explanation:

A exponential expression is given to us. And we need to simplify and find out the value. Here we will use some properties of exponents as ,

$\boxed{\begin{array}{c}\red{\dashrightarrow} \sf a^m \times a^n = a^{m+n} \\ \\ \red{\dashrightarrow} \sf (a^m)^n = a^{mn} \\\\\red{\dashrightarrow} \sf a^{-m }=\dfrac{1}{a^m} \\\\\red{\dashrightarrow} \sf a^m \div a^n = a^{m-n} \end{array}}$

Now here the given expression is :-

$\sf \red{\dashrightarrow} \bigg(\dfrac{2}{7}\bigg)^2 \times \bigg(\dfrac{7}{2}\bigg)^{-3} \div \left\{ \left( \dfrac{7}{5}\right)^{-2}\right\}^{-4}$

• Now remove the negative power of the second term by inversing the numerator and denominator. And further simplify by adding power of 1st and 2nd term .

$\sf \red{\dashrightarrow} \bigg(\dfrac{2}{7}\bigg)^2 \times \bigg(\dfrac{2}{7}\bigg)^{3} \div \left\{ \left( \dfrac{7}{5}\right)^{-2}\right\}^{-4} \\\\ \sf \red{\dashrightarrow} \bigg(\dfrac{2}{7}\bigg)^{3+2}\div \left\{ \left( \dfrac{7}{5}\right)^{-2}\right\}^{-4}$

• On looking at The third term , its power can be multiplied inside and outside the bracket.

$\sf \red{\dashrightarrow} \bigg(\dfrac{2}{7}\bigg)^5 \div \bigg(\dfrac{7}{5}\bigg)^{8} \\\\\sf \red{\dashrightarrow} \bigg(\dfrac{2}{7}\bigg)^5 \times \bigg(\dfrac{5}{7}\bigg)^8 \\\\ \sf \red{\dashrightarrow} \dfrac{ 2^5\times 5^8}{7^{13}}$

We needed to write the answer in expotential form with positive exponents . Therefore this is our required answer !