Find the positive solution of the equation. 5x^((7)/(5))-27=10485733 Answer:

Add 27 to both sides: Add 27 to both sides of the equation to isolate the term with the variable on one side. 5x^(7/5) - 27 + 27 = 10485733 + 27Simplify both sides: Simplify both sides of the equation. 5x^(7/5) = 10485760Divide by 5: Divide both sides of the equation by 5 to solve for x^(7/5). x^(7/5) = 10485760 / 5Calculate division result: Calculate the division on the right side of the equation. x^(7/5) = 2097152Raise to power of 5/7: Raise both sides of the equation to the power of 5/7 to solve for x. (x^(7/5))^(5/7) = 2097152^(5/7)Simplify using exponent property: Simplify the left side of the equation using the property of exponents (a^(m/n))^n = a^m. x = 2097152^(5/7)Calculate right side: Calculate the right side of the equation to find the value of x. x ≈ 2097152^(5/7)Use calculator: Use a calculator to find the value of 2097152^(5/7). x ≈ 128

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Grade 7

Powers with negative bases

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Q. Find the positive solution of the equation.

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5 x^{\frac{7}{5}}-27=10485733

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Answer:

Add $27$ to both sides: Add $27$ to both sides of the equation to isolate the term with the variable on one side. $\newline$ $5x^{\frac{7}{5}} - 27 + 27 = 10485733 + 27$
Simplify both sides: Simplify both sides of the equation. $5x^{7/5} = 10485760$
Divide by $5$ : Divide both sides of the equation by $5$ to solve for $x^{\frac{7}{5}}$ . $\newline$ $x^{\frac{7}{5}} = \frac{10485760}{5}$
Calculate division result: Calculate the division on the right side of the equation. $x^{\frac{7}{5}} = 2097152$
Raise to power of $5$ / $7$ : Raise both sides of the equation to the power of $5/7$ to solve for $x$ . $(x^{7/5})^{5/7} = 2097152^{5/7}$
Simplify using exponent property: Simplify the left side of the equation using the property of exponents $(a^{m/n})^n = a^m$ . $x = 2097152^{5/7}$
Calculate right side: Calculate the right side of the equation to find the value of $x$ . $x \approx 2097152^{(5/7)}$
Use calculator: Use a calculator to find the value of $2097152^{5/7}$ . $x \approx 128$