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5^(2(x-1))×5^(x+1)=0.04

$5^{2(x-1)} \times 5^{x+1}=0.04$

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Multiply and divide rational numbers

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Q.

5^{2(x-1)} \times 5^{x+1}=0.04

Simplify the equation: Step $1$ : Simplify the equation using properties of exponents. $\newline$ We know that when multiplying like bases, we add the exponents. So, $5^{2(x-1)} \times 5^{x+1}$ becomes $5^{2x - 2 + x + 1} = 5^{3x - 1}$ .
Set equal to $0.04$ : Step $2$ : Set the simplified expression equal to $0.04$ and solve for $x$ . We have $5^{3x - 1} = 0.04$ . We know that $0.04$ can be written as $\frac{1}{25}$ , which is the same as $5^{-2}$ . So, $5^{3x - 1} = 5^{-2}$ .
Set exponents equal: Step $3$ : Since the bases are the same, set the exponents equal to each other. $3x - 1 = -2$ .
Solve for x: Step $4$ : Solve for x. $\newline$ Add $1$ to both sides: $3x - 1 + 1 = -2 + 1$ , $\newline$ $3x = -1$ , $\newline$ Divide by $3$ : $x = -\frac{1}{3}$ .

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