Question

Simplify and write the answer in the exponential form.

$\left(\frac{7^{20}}{7^{15}}\right)\times 7^4$

Answer 1

Hint: We know the law of exponents that is powers with same base: $x^a÷x^b=x^{a-b}$ And $x^a\times x^b=x^{a+b}$

Step 1: Given expression: $\left(\frac{7^{20}}{7^{15}}\right)\times 7^4$

Step 2: Solution:

Using the above law:

$$\begin{gathered} \left(\frac{7^{20}}{7^{15}}\right)\times 7^4=\left(7^{20-15}\right)\times 7^4;\left\{\left(\frac{x^a}{x^b}\right)=x^{a-b}\right\} \\ =\left(7^5\right)\times 7^4;\{x^a\times x^b=x^{a+b}\} \\ ={\left(7\right)}^{5+4} \\ ={\left(7\right)}^9 \end{gathered}$$

${\left(7\right)}^9$, this is the required exponential form.

Hence ${\left(7\right)}^9$, this is the required exponential form.