Simplify. Express your answer using exponents.
(10a^4b^7c^8)^3
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Simplify. Express your answer using exponents. (10a^4b^7c^8)^3 Submit
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To simplify the expression ((10a^4b^7c^8)^3), we will apply the power of a product and power of a power rules in exponents.
1. Apply the power to each factor inside the parentheses:
((10)^3), ((a^4)^3), ((b^7)^3), and ((c^8)^3).
2. Calculate each part:
– (10^3 = 1000)
– ((a^4)^3 = a^{4 cdot 3} = a^{12})
– ((b^7)^3 = b^{7 cdot 3} = b^{21})
– ((c^8)^3 = c^{8 cdot 3} = c^{24})
3. Combine everything:
So, the expression simplifies to:
[
1000a^{12}b^{21}c^{24}
]
Your final answer is:
[
1000a^{12}b^{21}c^{24}
]
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