5272道题目5525 条题源记录 · 相同内容已合并
根式与有理指数进阶
\( \sqrt{(\frac{1}{9}t)^{5}}=\frac{1}{243}(\sqrt[9]{t})^{k} \)
In the given equation, \( t>0 \), and k is a constant. What is the value of k?
In the given equation, \( t>0 \), and k is a constant. What is the value of k?
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根式与有理指数挑战
\( p=\sqrt{12c}-25 \)
The given equation relates the variables p and c, where c is positive. Which equation correctly expresses c in terms of p?
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根式与有理指数进阶
If \( \sqrt{x-1}=2 \), what is the value of \( (x−1) \)?
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根式与有理指数挑战
If \( \sqrt{x-5}=8 \) , what is the value of \( (x−5) \)?
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根式与有理指数进阶
\( \frac{x^2}{\sqrt{x^2-c^2}}=\frac{c^2}{\sqrt{x^2-c^2}}+39 \)
In the given equation, c is a positive constant. Which of the following is one of the solutions to the given equation?
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根式与有理指数挑战
\( \sqrt[3]{p^{2}}=t^{\frac{9}{7}} \)
In the given equation, \( p>1 \) and \( t>1 \) . If \( t=p^{3n-1} \), where n is a constant, what is the value of n?
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根式与有理指数进阶
The function f is defined by \( f\left(x\right)=a\sqrt{x+b} \) , where a and b are constants. In the xy-plane, the graph of\( y=f\left(x\right) \) passes through the point (-24, 0), and f (24)< 0. Which of the following must be true?
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根式与有理指数进阶
If\( 4\sqrt{2x}=16 \) , what is the value of 6x?
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根式与有理指数进阶
Which expression is equivalent to \( a^{\frac{11}{12}} \) , where \( a>0 \) ?
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根式与有理指数进阶
\( \sqrt{\left(x-2\right)^2}=\sqrt{3x+34} \)
What is the smallest solution to the given equation?
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根式与有理指数挑战
The expression \( \frac{x^{−2}y^{\frac{1}{2}}}{2} \) , where x > 1 and y > 1, is equivalent to which of the following?
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根式与有理指数挑战
The expression \( 6\sqrt[5]{3^{5}x^{45}} \) •\( \sqrt[8]{2^{8}x} \) is equivalent to axb, where a and b are positive constants and x > 1. What is the value of a + b ?
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