 Oakey1w

2022-06-29

Pre-Algebra Fractional Exponent Question
Why does ${t}^{\frac{3}{2}}\cdot {t}^{\frac{1}{2}}={t}^{2}$?
What I tried to do was multiply the exponents together $\frac{3}{2}\cdot \frac{1}{2}=\frac{3}{4}$ so my final answer was ${t}^{\frac{3}{4}}$ but according to my Wileyplus homework it is ${t}^{2}$. lodosr

Expert

When multiplying two of the same number raised to exponents (such as ${x}^{\frac{3}{2}}$ times ${x}^{\frac{1}{2}}$) you add the exponents.
${x}^{a}\cdot {x}^{b}={x}^{a+b}$
Only when raising a number to an exponent, and raising the result to an exponent do you multiply exponents together.
$\left({x}^{a}{\right)}^{b}={x}^{a\cdot b}$
Note: $\left({x}^{a}{\right)}^{b}\ne {x}^{\left({a}^{b}\right)}$ flightwingsd2

Expert

Just remember this:
${a}^{b}+{a}^{c}={a}^{b+c}$
$a=t,\phantom{\rule{thinmathspace}{0ex}}b=3/2,\phantom{\rule{thinmathspace}{0ex}}c=1/2$
and
${t}^{3}/2+{t}^{1}/2={t}^{1/2+3/2}={t}^{4}/2={t}^{2}$
hope this helped!

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