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

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

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

simplify

\frac{( 8 x ^{6} \cdot z ^{4} + 4 x ^{4} \cdot z ^{2} )}{( 4 x ^{2} \cdot 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{( a ^{5} + b ^{5} )}{( a + b )}

\frac{a ^{4}}{a ^{3}}

s^{3} sin (2 t + \frac{7}{8}) + 3 sin (2 t - \frac{7}{8})

a^{6} b^{3} - 1

5 x - x y + 15 - 3 y

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