Question
Simplify and express the number in exponential form: $\frac{2^{8} \times a^{5}}{4^{3} \times a^{3}}$
✓
Answer
By the law of exponents we have,
$\left(x^m\right)^n=x^{m n}$
$\frac{x^m}{x^n}=x^{m-n}$
By applying these laws we have
$\frac{2^8 \times a^5}{4^3 \times a^3}=\frac{2^8 \times a^5}{\left(2^2\right)^3 \times a^3}=\frac{2^8 \times a^5}{2^{2 \times 3} \times a^3}$
$=\frac{2^8 \times a^5}{2^6 \times a^3}=2^{8-6} \times a^{5-3}=2^2 \times a^2=(2 a)^2$
$=4 a^2$
Hence $\frac{2^8 \times \mathrm{a}^5}{4^3 \times \mathrm{a}^3}=4 \mathrm{a}^2$
$\left(x^m\right)^n=x^{m n}$
$\frac{x^m}{x^n}=x^{m-n}$
By applying these laws we have
$\frac{2^8 \times a^5}{4^3 \times a^3}=\frac{2^8 \times a^5}{\left(2^2\right)^3 \times a^3}=\frac{2^8 \times a^5}{2^{2 \times 3} \times a^3}$
$=\frac{2^8 \times a^5}{2^6 \times a^3}=2^{8-6} \times a^{5-3}=2^2 \times a^2=(2 a)^2$
$=4 a^2$
Hence $\frac{2^8 \times \mathrm{a}^5}{4^3 \times \mathrm{a}^3}=4 \mathrm{a}^2$
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