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TaeKwonDoIsDead

Answer:

[tex]8m^4n^5[/tex]

Step-by-step explanation:

cube root is basically taking to the power of  [tex]\frac{1}{3}[/tex]

Also, there is a property that is  [tex](x^m)^n=x^{mn}[/tex]

We can use these and find the cube root of the expression:

[tex](512m^{12}n^{15})^{\frac{1}{3}}\\=(512)^{\frac{1}{3}}*(m^{12})^{\frac{1}{3}}*(n^{15})^{\frac{1}{3}}\\=8*m^{\frac{12}{3}}*n^{\frac{15}{3}}\\=8*m^4 * n^5[/tex]

Thus, third answer chioce is right.

Answer:

C. 8m^4n^5[/tex]

Step-by-step explanation:

We are given [tex]\sqrt[3]{512m^{12}n^{15}  }[/tex]

The cube root is nothing but the power of [tex]\frac{1}{3}[/tex]

Now we have to write 512 as the power 3.

512 = 8.8.8 = [tex]8^{3}[/tex]

So, [tex]\sqrt[3]{512m^{12}n^{15}  }[/tex] = [tex](8^{3}.m^{12}.n^{15})   ^{\frac{1}{3}}[/tex]

We know that the exponent property: [tex](a^{m} )^n= a^{mn}[/tex]

Using this property, we can simplify the exponents.

= [tex]8.m^{4} .n^5 = 8m^4n^5[/tex]

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