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Simplify c^4(xc^4) ^4 s^4 x Write your answer with only positive exponents

Simplify C4xc4 4 S4 X Write Your Answer With Only Positive Exponents class=

Sagot :

Firstly, let's put the varibles without exponent the exponent 1:

[tex]c^4(xc^4)^4s^4x=c^4(x^1c^4)^4s^4x^1[/tex]

Now, we can apply the Power to a Power rule:

[tex](a^bc^d)^f=a^{b\cdot f}c^{d\cdot f}[/tex][tex]c^4(x^1c^4)^4s^4x^1=c^4x^{1\cdot4}c^{4\cdot4}s^4x^1=c^4x^4c^{16}s^4x^1[/tex]

Now, we can rearregent them to get the variables paired:

[tex]c^4x^4c^{16}s^4x^1=c^4c^{16}x^4x^1s^4[/tex]

And now we use the Power of a Product rule:

[tex]a^ba^c=a^{b+c}[/tex]

So:

[tex]c^4c^{16}x^4x^1s^4=c^{4+16}x^{4+1}s^4=c^{20}x^5s^4[/tex]

So, the simplification is:

[tex]c^{20}x^5s^4[/tex]

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