Use the laws of exponents to simplify the expressions 44.243.7

Question

Use the laws of exponents to simplify the expressions  44.243.7

wheezym · Accepted Answer

We can simplify the exponents using the laws of exponents . Here we can use the laws of exponents such as
$a^{m} \cdot a^{n} = a^{m n}$
$\frac{a^{m}}{a^{n}} = a^{m - n}$
Also we can use radical to exponent conversion forms to simplify the exponent terms,
The conversion formula $a^{\frac{1}{2}} = \sqrt{a}$ can be used here . In general we have the conversion formula of exponent to radical as, $a^{\frac{1}{n}} = \sqrt[n]{a}$
Consider the expression $\frac{4^{4.2}}{4^{3.7}}$
We can use the exponent law $\frac{a^{m}}{a^{n}} = a^{m - n}$
For $a = 4, m = 4.2, n = 3.7$ from the exponent law we get,
$\frac{4^{4.2}}{4^{3.7}} = 4^{4.2 - 3.7}$
$= 4^{0.5}$
$= 4^{\frac{1}{2}}$
$= \sqrt{4}$
$= 2$
Hence we have the simplest form 2 .

Use the laws of exponents to simplify the expressions \frac{4^{4.2}}{4^{3}

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