Find the value of diamond : ((7^(diamond))^(6))^(2)=7^(-36) diamond=◻

Identify Equation and Property: Identify the given equation and the property of exponents that when raising a power to another power, you multiply the exponents. The given equation is ((7^(diamond))^6)^2 = 7^(-36). Using the property of exponents, we can simplify the left side of the equation by multiplying the exponents: (diamond * 6) * 2.Simplify Left Side: Simplify the multiplication of the exponents on the left side of the equation. (diamond * 6) * 2 = diamond * 12. Now the equation looks like 7^(diamond * 12) = 7^(-36).Multiply Exponents: Since the bases are the same on both sides of the equation, we can set the exponents equal to each other. This gives us diamond * 12 = -36.Set Exponents Equal: Solve for ＂diamond＂ by dividing both sides of the equation by 12. diamond * 12 / 12 = -36 / 12. This simplifies to diamond = -3.

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Q. Find the value of

\diamond

\newline

(7^{\diamond})^{6})^{2}=7^{-36}

\newline

\diamond = \square

Identify Equation and Property: Identify the given equation and the property of exponents that when raising a power to another power, you multiply the exponents. $\newline$ The given equation is $((7^{\text{diamond}})^6)^2 = 7^{-36}$ . $\newline$ Using the property of exponents, we can simplify the left side of the equation by multiplying the exponents: $(\text{diamond} \times 6) \times 2$ .
Simplify Left Side: Simplify the multiplication of the exponents on the left side of the equation. $\newline$ $(\diamond \times 6) \times 2 = \diamond \times 12$ . $\newline$ Now the equation looks like $7^{(\diamond \times 12)} = 7^{(-36)}$ .
Multiply Exponents: Since the bases are the same on both sides of the equation, we can set the exponents equal to each other. $\newline$ This gives us $\diamond \times 12 = -36$ .
Set Exponents Equal: Solve for ＂diamond＂ by dividing both sides of the equation by $12$ . $\newline$ $\text{diamond} \times \frac{12}{12} = \frac{-36}{12}.$ $\newline$ This simplifies to $\text{diamond} = -3$ .