Oakey1w

Answered

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 ${t}^{2}$.

Can someone please explain?

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 ${t}^{2}$.

Can someone please explain?

Answer & Explanation

lodosr

Expert

2022-06-30Added 24 answers

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.

$({x}^{a}{)}^{b}={x}^{a\cdot b}$

Note: $({x}^{a}{)}^{b}\ne {x}^{({a}^{b})}$

${x}^{a}\cdot {x}^{b}={x}^{a+b}$

Only when raising a number to an exponent, and raising the result to an exponent do you multiply exponents together.

$({x}^{a}{)}^{b}={x}^{a\cdot b}$

Note: $({x}^{a}{)}^{b}\ne {x}^{({a}^{b})}$

flightwingsd2

Expert

2022-07-01Added 5 answers

Just remember this:

${a}^{b}+{a}^{c}={a}^{b+c}$

so in your problem,

$a=t,\phantom{\rule{thinmathspace}{0ex}}b=3/2,\phantom{\rule{thinmathspace}{0ex}}c=1/2$

and

${t}^{3}/2+{t}^{1}/2={t}^{1/2+3/2}={t}^{4}/2={t}^{2}$

hope this helped!

${a}^{b}+{a}^{c}={a}^{b+c}$

so in your problem,

$a=t,\phantom{\rule{thinmathspace}{0ex}}b=3/2,\phantom{\rule{thinmathspace}{0ex}}c=1/2$

and

${t}^{3}/2+{t}^{1}/2={t}^{1/2+3/2}={t}^{4}/2={t}^{2}$

hope this helped!

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