Pre-Algebra Fractional Exponent Question

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?

Answer 1

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: $(x^{a})^{b} \neq x^{(a^b)}$

Answer 2

Just remember this: $$a^b+a^c= a^{b+c}$$ so in your problem, $$a=t, \, b=3/2, \, c=1/2$$ and $$ t^3/2+t^1/2= t^{1/2+3/2}= t^4/2=t^2$$

hope this helped!