Question

Using laws of exponents, simplify and write the answer in exponential form:

$(2^{20}÷2^{15})\times 2^3$

Answer 1

Compute the required value:

We know that by the rule of dividing the powers with the same base, we have

${\mathrm{a}}^{\mathrm{m}}÷{\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}$

So,$(2^{20}÷2^{15})$ can be simplified as

$\begin{array}{rcl}{2}^{20}÷2^{15}& =& 2^{20-15}\\ & =& 2^5\end{array}$

Now by the rule of multiplying the powers with the same base $a^m\times a^n=a^{m+n}$

$\begin{array}{rcl}{2}^5\times 2^3& =& 2^{5+3}\\ & =& 2^8\end{array}$ can be simplified as,

Hence,Using laws of exponents, $(2^{20}÷2^{15})\times 2^3=2^8$.