How do you simplify the fifth root of t (or $t^{\frac{1}{5}}$ $t^(1/5)$ ) multiplied by radical ( $16 t^{5}$ $16t^5$ )?

Question

How do you simplify the fifth root of t (or $t^{\frac{1}{5}}$ $t^(1/5)$ ) multiplied by radical ( $16 t^{5}$ $16t^5$ )?

1 Answer

Impact of this question

1557 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-03-22T17:50:40

I assume that "radical" here means square root.

$t^{\frac{1}{5}} \cdot \sqrt{16 t^{5}} = t^{\frac{1}{5}} \sqrt{16} {\sqrt{t}}^{5} = 4 t^{\frac{1}{5}} \sqrt{t^{5}}$ $t^(1/5)*sqrt(16t^5)=t^(1/5)sqrt16sqrtt^5=4t^(1/5)sqrt(t^5)$

Now as a general definition: $\sqrt[n]{x^{m}} = x^{\frac{m}{n}}$ $root(n)(x^m)=x^(m/n)$ . So $\sqrt{t^{5}} = t^{\frac{5}{2}}$ $sqrt(t^5)=t^(5/2)$

The expression now becomes:

$t^{\frac{1}{5}} \cdot \sqrt{16 t^{5}} = 4 t^{\frac{1}{5}} \sqrt{t^{5}} = 4 t^{\frac{1}{5}} t^{\frac{5}{2}}$ $t^(1/5)*sqrt(16t^5)=4t^(1/5)sqrt(t^5)=4t^(1/5)t^(5/2)$

An important property of exponents assures us that:
$x^{n} x^{m} = x^{n + m}$ $x^nx^m=x^(n+m)$ .

So we can simplify $t^{\frac{1}{5}} t^{\frac{5}{2}}$ $t^(1/5)t^(5/2)$ by adding $\frac{1}{5} + \frac{5}{2} = \frac{27}{10}$ $1/5+5/2=27/10$ .

$t^{\frac{1}{5}} \cdot \sqrt{16 t^{5}} = 4 t^{\frac{1}{5}} t^{\frac{5}{2}} = 4 t^{\frac{27}{10}} = 4 \sqrt[10]{t^{27}}$ $t^(1/5)*sqrt(16t^5)=4t^(1/5)t^(5/2)=4t^(27/10)=4 root(10)(t^27)$ .

Science

Math

Humanities

... and beyond

How do you simplify the fifth root of t (or $t^{\frac{1}{5}}$ $t^(1/5)$ ) multiplied by radical ( $16 t^{5}$ $16t^5$ )?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify the fifth root of t (or t15t^(1/5)) multiplied by radical (16t516t^5)?

1 Answer

Related questions

Impact of this question

How do you simplify the fifth root of t (or $t^{\frac{1}{5}}$ $t^(1/5)$ ) multiplied by radical ( $16 t^{5}$ $16t^5$ )?