Simplify. Express your answer using exponents.
(3j²k⁵m⁵)²
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To simplify the expression (3j²k⁵m⁵)², you need to apply the power of a power property, which states that when you raise a power to another power, you multiply the exponents.
Here’s the step-by-step simplification:
1. Square the Coefficient: The coefficient 3 gets squared:
[
3² = 9
]
2. Square Each Variable:
– For (j²), you calculate ( (j²)² = j^{2 cdot 2} = j^{4} ).
– For (k⁵), you calculate ( (k⁵)² = k^{5 cdot 2} = k^{10} ).
– For (m⁵), you calculate ( (m⁵)² = m^{5 cdot 2} = m^{10} ).
3. Combine All Parts: Now combine the squared coefficient and the squared variables:
[
9j^{4}k^{10}m^{10}
]
So, the simplified expression is:
[
boxed{9j^{4}k^{10}m^{10}}
]
This shows the original expression simplified with exponents. If you have more questions or need further assistance, feel free to ask!