What is (20sqrt(z^6))/(sqrt(16z^7)) ?

The solution to (20sqrt(z^6))/(sqrt(16z^7)) is 5/(sqrt(z))

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simplify (20sqrt(z^6))/(sqrt(16z^7))

simplify

\frac{20 z ^{6}}{16 z ^{7}}

\frac{5}{z}

Solution steps

\frac{20 z ^{6}}{16 z ^{7}}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

16 z^{7} = 16 z^{7}

= \frac{20 z ^{6}}{16 z ^{7}}

Factor the number:

20 = 4 \cdot 5

= \frac{4 \cdot 5 z ^{6}}{16 z ^{7}}

16 = 4

= \frac{4 \cdot 5 z ^{6}}{4 z ^{7}}

Cancel the common factor:

4

= \frac{5 z ^{6}}{z ^{7}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

z^{7} = z^{6} z

= \frac{5 z ^{6}}{z ^{6} z}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

z^{6} z = z^{6} z

= \frac{5 z ^{6}}{z ^{6} z}

Cancel the common factor:

z^{6}

= \frac{5}{z}

\frac{2 ( n ^{3} ) ^{4}}{6 n ^{6}}

\frac{18}{162}

- 0 - 2

(3^{5})^{4}

- 8 m - m

What is (20sqrt(z^6))/(sqrt(16z^7)) ?
The solution to (20sqrt(z^6))/(sqrt(16z^7)) is 5/(sqrt(z))