What is (8x^6z^4+4x^4z^2)/(4x^2z) ?

The solution to (8x^6z^4+4x^4z^2)/(4x^2z) is x^2z(2x^2z^2+1)

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simplify (8x^6z^4+4x^4z^2)/(4x^2z)

simplify

\frac{8 x ^{6} z ^{4} + 4 x ^{4} z ^{2}}{4 x ^{2} z}

x^{2} z (2 x^{2} z^{2} + 1)

Solution steps

\frac{8 x ^{6} z ^{4} + 4 x ^{4} z ^{2}}{4 x ^{2} z}

Factor

8 x^{6} z^{4} + 4 x^{4} z^{2} : 4 x^{4} z^{2} (2 x^{2} z^{2} + 1)

= \frac{4 x ^{4} z ^{2} ( 2 x ^{2} z ^{2} + 1 )}{4 x ^{2} z}

Cancel the common factor:

4

= \frac{x ^{4} z ^{2} ( 2 x ^{2} z ^{2} + 1 )}{x ^{2} z}

Apply exponent rule:

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

x^{4} = x^{2} x^{2}

= \frac{x ^{2} x ^{2} z ^{2} ( 2 x ^{2} z ^{2} + 1 )}{x ^{2} z}

Cancel the common factor:

x^{2}

= \frac{x ^{2} z ^{2} ( 2 x ^{2} z ^{2} + 1 )}{z}

Apply exponent rule:

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

z^{2} = zz

= \frac{x ^{2} zz ( 2 x ^{2} z ^{2} + 1 )}{z}

Cancel the common factor:

z

= x^{2} z (2 x^{2} z^{2} + 1)

\frac{- 4}{- 16}

\frac{x ^{7}}{x ^{1}}

\frac{20000}{3}

\frac{1}{20} + \frac{1}{30} + \frac{1}{60}

8 x^{4} - 128

What is (8x^6z^4+4x^4z^2)/(4x^2z) ?
The solution to (8x^6z^4+4x^4z^2)/(4x^2z) is x^2z(2x^2z^2+1)