IDNLearn.com connects you with experts who provide accurate and reliable answers. Join our community to receive prompt, thorough responses from knowledgeable experts.
Sagot :
Let's simplify each expression step-by-step using the properties of exponents:
### Expression 1: [tex]\(\left(-8 c^0\right)^5\)[/tex]
1. Understanding [tex]\(c^0\)[/tex]: By the property of exponents, any nonzero number raised to the power of 0 is 1. Therefore, [tex]\(c^0 = 1\)[/tex].
2. Simplify the Expression:
[tex]\[ \left(-8 c^0\right)^5 = \left(-8 \cdot 1\right)^5 = \left(-8\right)^5 \][/tex]
3. Calculate [tex]\(\left(-8\right)^5\)[/tex]:
[tex]\[ \left(-8\right)^5 = (-8) \cdot (-8) \cdot (-8) \cdot (-8) \cdot (-8) = -32768 \][/tex]
So, the simplified expression is:
[tex]\[ -32768 \][/tex]
### Expression 2: [tex]\((-9 x)^3 - 9 x^3\)[/tex]
1. Simplify [tex]\((-9x)^3\)[/tex]:
[tex]\[ (-9x)^3 = (-9)^3 \cdot x^3 = -729 \cdot x^3 = -729x^3 \][/tex]
2. Subtract [tex]\(9x^3\)[/tex] from [tex]\(-729x^3\)[/tex]:
[tex]\[ (-729x^3) - (9x^3) = -729x^3 - 9x^3 \][/tex]
3. Combine like terms:
[tex]\[ -729x^3 - 9x^3 = -738x^3 \][/tex]
So, the simplified expression is:
[tex]\[ -738x^3 \][/tex]
### Expression 3: [tex]\(5 d^0 + 6 d^0\)[/tex]
1. Understanding [tex]\(d^0\)[/tex]: By the property of exponents, any nonzero number raised to the power of 0 is 1. Therefore, [tex]\(d^0 = 1\)[/tex].
2. Simplify the Expression:
[tex]\[ 5 d^0 + 6 d^0 = 5 \cdot 1 + 6 \cdot 1 = 5 + 6 \][/tex]
So, the simplified expression is:
[tex]\[ 11 \][/tex]
### Expression 4: [tex]\(\left(\frac{2 x^2 + 7 x + 4}{9}\right)^0\)[/tex]
1. Understanding [tex]\(\left(\text{anything}\right)^0\)[/tex]: By the property of exponents, any nonzero expression raised to the power of 0 is 1.
2. Simplify the Expression:
[tex]\[ \left(\frac{2 x^2 + 7 x + 4}{9}\right)^0 = 1 \][/tex]
So, the simplified expression is:
[tex]\[ 1 \][/tex]
### Summary Table:
[tex]\[ \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{Properties of Exponents} \\ \hline Simplify the following expressions where variables are nonzero numbers \\ \hline Original Expression & Simplified Expression \\ \hline \(\left(-8 c^0\right)^5\) & \(-32768\) \\ \hline \((-9 x)^3 - 9 x^3\) & \(-738x^3\) \\ \hline \(5 d^0 + 6 d^0\) & \(11\) \\ \hline \(\left(\frac{2 x^2 + 7 x + 4}{9}\right)^0\) & \(1\) \\ \hline \end{tabular} \][/tex]
### Expression 1: [tex]\(\left(-8 c^0\right)^5\)[/tex]
1. Understanding [tex]\(c^0\)[/tex]: By the property of exponents, any nonzero number raised to the power of 0 is 1. Therefore, [tex]\(c^0 = 1\)[/tex].
2. Simplify the Expression:
[tex]\[ \left(-8 c^0\right)^5 = \left(-8 \cdot 1\right)^5 = \left(-8\right)^5 \][/tex]
3. Calculate [tex]\(\left(-8\right)^5\)[/tex]:
[tex]\[ \left(-8\right)^5 = (-8) \cdot (-8) \cdot (-8) \cdot (-8) \cdot (-8) = -32768 \][/tex]
So, the simplified expression is:
[tex]\[ -32768 \][/tex]
### Expression 2: [tex]\((-9 x)^3 - 9 x^3\)[/tex]
1. Simplify [tex]\((-9x)^3\)[/tex]:
[tex]\[ (-9x)^3 = (-9)^3 \cdot x^3 = -729 \cdot x^3 = -729x^3 \][/tex]
2. Subtract [tex]\(9x^3\)[/tex] from [tex]\(-729x^3\)[/tex]:
[tex]\[ (-729x^3) - (9x^3) = -729x^3 - 9x^3 \][/tex]
3. Combine like terms:
[tex]\[ -729x^3 - 9x^3 = -738x^3 \][/tex]
So, the simplified expression is:
[tex]\[ -738x^3 \][/tex]
### Expression 3: [tex]\(5 d^0 + 6 d^0\)[/tex]
1. Understanding [tex]\(d^0\)[/tex]: By the property of exponents, any nonzero number raised to the power of 0 is 1. Therefore, [tex]\(d^0 = 1\)[/tex].
2. Simplify the Expression:
[tex]\[ 5 d^0 + 6 d^0 = 5 \cdot 1 + 6 \cdot 1 = 5 + 6 \][/tex]
So, the simplified expression is:
[tex]\[ 11 \][/tex]
### Expression 4: [tex]\(\left(\frac{2 x^2 + 7 x + 4}{9}\right)^0\)[/tex]
1. Understanding [tex]\(\left(\text{anything}\right)^0\)[/tex]: By the property of exponents, any nonzero expression raised to the power of 0 is 1.
2. Simplify the Expression:
[tex]\[ \left(\frac{2 x^2 + 7 x + 4}{9}\right)^0 = 1 \][/tex]
So, the simplified expression is:
[tex]\[ 1 \][/tex]
### Summary Table:
[tex]\[ \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{Properties of Exponents} \\ \hline Simplify the following expressions where variables are nonzero numbers \\ \hline Original Expression & Simplified Expression \\ \hline \(\left(-8 c^0\right)^5\) & \(-32768\) \\ \hline \((-9 x)^3 - 9 x^3\) & \(-738x^3\) \\ \hline \(5 d^0 + 6 d^0\) & \(11\) \\ \hline \(\left(\frac{2 x^2 + 7 x + 4}{9}\right)^0\) & \(1\) \\ \hline \end{tabular} \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.
