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Answer :
To find the cube root of [tex]\( 8x^{27} \)[/tex], let's break it down step by step:
1. Find the cube root of the numerical part:
- The number 8 can be expressed as [tex]\( 2^3 \)[/tex]. The cube root of 8 is the number that, when multiplied by itself three times, equals 8. That number is 2.
2. Find the cube root of the algebraic part:
- For the algebraic expression [tex]\( x^{27} \)[/tex], the cube root can be found by dividing the exponent by 3. This is because [tex]\( (x^a)^{\frac{1}{3}} = x^{\frac{a}{3}} \)[/tex].
- So, [tex]\( \left(x^{27}\right)^{\frac{1}{3}} = x^{\frac{27}{3}} = x^9 \)[/tex].
3. Combine the results:
- Now, combine the results of the numerical and algebraic parts. The cube root of [tex]\( 8x^{27} \)[/tex] is [tex]\( 2x^9 \)[/tex].
Therefore, the answer is [tex]\( 2x^9 \)[/tex].
1. Find the cube root of the numerical part:
- The number 8 can be expressed as [tex]\( 2^3 \)[/tex]. The cube root of 8 is the number that, when multiplied by itself three times, equals 8. That number is 2.
2. Find the cube root of the algebraic part:
- For the algebraic expression [tex]\( x^{27} \)[/tex], the cube root can be found by dividing the exponent by 3. This is because [tex]\( (x^a)^{\frac{1}{3}} = x^{\frac{a}{3}} \)[/tex].
- So, [tex]\( \left(x^{27}\right)^{\frac{1}{3}} = x^{\frac{27}{3}} = x^9 \)[/tex].
3. Combine the results:
- Now, combine the results of the numerical and algebraic parts. The cube root of [tex]\( 8x^{27} \)[/tex] is [tex]\( 2x^9 \)[/tex].
Therefore, the answer is [tex]\( 2x^9 \)[/tex].
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