Find the value of diamond : (n^(2)n^(-6)n^(diamond))^(8)=n^(24)

Simplify Exponents: First, we need to simplify the expression inside the parentheses by adding the exponents of n, since they are being multiplied together. n^(2) * n^(-6) * n^(diamond) = n^(2 - 6 + diamond) = n^(diamond - 4)Raise to Power: Next, we raise the simplified expression to the power of 8, which means we multiply the exponent (diamond - 4) by 8. (n^(diamond - 4))^(8) = n^((diamond - 4) * 8)Set Equal to n^24: Now we set the expression equal to n^(24) to find the value of the exponent ＂diamond＂. n^((diamond - 4) * 8) = n^(24)Solve for Diamond: Since the bases are the same (n), we can set the exponents equal to each other to solve for ＂diamond＂. (diamond - 4) * 8 = 24Find Diamond Value: We divide both sides of the equation by 8 to solve for ＂diamond＂. (diamond - 4) = 24 / 8 diamond - 4 = 3Finally, we add 4 to both sides of the equation to find the value of ＂diamond＂. diamond = 3 + 4 diamond = 7

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Find the value of
diamond :

(n^(2)n^(-6)n^(diamond))^(8)=n^(24)

Find the value of $\diamond$ : $\newline$ $\left(n^{2} n^{-6} n^{\diamond}\right)^{8}=n^{24}$

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Q. Find the value of

\diamond

\newline

\left(n^{2} n^{-6} n^{\diamond}\right)^{8}=n^{24}

Simplify Exponents: First, we need to simplify the expression inside the parentheses by adding the exponents of $n$ , since they are being multiplied together. $n^{2} \times n^{-6} \times n^{\diamond} = n^{2 - 6 + \diamond} = n^{\diamond - 4}$
Raise to Power: Next, we raise the simplified expression to the power of $8$ , which means we multiply the exponent ( $\text{diamond} - 4$ ) by $8$ . $(n^{(\text{diamond} - 4)})^{8} = n^{((\text{diamond} - 4) \cdot 8)}$
Set Equal to $n^{24}$ : Now we set the expression equal to $n^{24}$ to find the value of the exponent ＂diamond＂. $\newline$ $n^{(\text{diamond} - 4) \times 8} = n^{24}$
Solve for Diamond: Since the bases are the same $n$ , we can set the exponents equal to each other to solve for ＂diamond＂. $(\text{diamond} - 4) \times 8 = 24$
Find Diamond Value: We divide both sides of the equation by $8$ to solve for ＂diamond＂. $\newline$ $(\text{diamond} - 4) = \frac{24}{8}$ $\newline$ $\text{diamond} - 4 = 3$
Find Diamond Value: We divide both sides of the equation by $8$ to solve for ＂diamond＂. $\newline$ $(\text{diamond} - 4) = \frac{24}{8}$ $\newline$ $\text{diamond} - 4 = 3$ Finally, we add $4$ to both sides of the equation to find the value of ＂diamond＂. $\newline$ $\text{diamond} = 3 + 4$ $\newline$ $\text{diamond} = 7$