The equation (x^(3+y))*x^(5)=x^(20) is true for all values of x. What is the value of y ?

Given Equation: We are given the equation: (x^(3+y))*x^(5)=x^(20) We need to find the value of y. According to the properties of exponents, when we multiply two exponents with the same base, we add the exponents. So, we can rewrite the left side of the equation as: x^(3+y+5) = x^(20)Rewriting with Exponents: Now we simplify the exponent on the left side by adding the constants: 3 + 5 = 8 So the equation becomes: x^(y+8) = x^(20)Simplify Exponents: Since the bases are the same and the equation holds for all values of x, we can equate the exponents: y + 8 = 20Solve for y: Now we solve for y by subtracting 8 from both sides of the equation: y = 20 - 8 y = 12

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Find derivatives using the chain rule I

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Q. The equation

\left(x^{3+y}\right) \cdot x^{5}=x^{20}

is true for all values of

x

. What is the value of

y

Given Equation: We are given the equation: $\newline$ $x^{(3+y)}\cdot x^{5}=x^{20}$ $\newline$ We need to find the value of $y$ . $\newline$ According to the properties of exponents, when we multiply two exponents with the same base, we add the exponents. $\newline$ So, we can rewrite the left side of the equation as: $\newline$ $x^{(3+y+5)} = x^{20}$
Rewriting with Exponents: Now we simplify the exponent on the left side by adding the constants: $\newline$ $3 + 5 = 8$ $\newline$ So the equation becomes: $\newline$ $x^{(y+8)} = x^{20}$
Simplify Exponents: Since the bases are the same and the equation holds for all values of $x$ , we can equate the exponents: $y + 8 = 20$
Solve for y: Now we solve for y by subtracting $8$ from both sides of the equation: $\newline$ $y = 20 - 8$ $\newline$ $y = 12$