Simplify. Express your answer using exponents.
(5h²j⁸k³)³
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Simplify. Express your answer using exponents. (5h²j⁸k³)³ Submit.
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To simplify the expression ((5h²j⁸k³)³), we need to apply the power of a product rule, which states that ((ab)^{n} = a^{n}b^{n}). This means we will raise each factor inside the parentheses to the power of 3.
1. Raise the coefficient:
[ 5^3 = 125 ]
2. Raise the variable (h²):
[ (h²)³ = h^{2 cdot 3} = h^6 ]
3. Raise the variable (j⁸):
[ (j⁸)³ = j^{8 cdot 3} = j^{24} ]
4. Raise the variable (k³):
[ (k³)³ = k^{3 cdot 3} = k^{9} ]
Now, combine all these results:
[
(5h²j⁸k³)³ = 125h^6j^{24}k^{9}
]
So, the simplified expression is:
[
boxed{125h^6j^{24}k^{9}}
]
This solution uses the exponentiation rule appropriately to simplify the expression. If you have more questions or need further explanation, feel free to ask!