اختبار إلكتروني: revision on nth roots and rational exponent
This worksheet provides a comprehensive review of nth roots and rational exponents. It covers converting between radical and exponential forms, simplifying complex algebraic expressions with fractional exponents, and solving radical equations by isolating the radical. Key concepts include identifying real roots for various indices and applying exponent laws to simplify products and quotients of terms with rational powers.
رقم الاختبار832
الصفالصف العاشر المتقدم
المادةرياضيات
الفصلالفصل الثالث
السنة الدراسية2025/2026
عدد الأسئلة17
إجمالي النقاط17
تاريخ الإضافة2026-04-21
الزيارات52
المعلم أو الناشرAmal Salman
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
Question 1
Points: 1
Rewrite into rational exponent form: \( \sqrt{10} \)
Explanation
A square root can be written as a rational exponent with an index of 2, so \( \sqrt{10} = 10^{1/2} \).
Question 2
Points: 1
Simplify: \( 32^{3/5} \)
Explanation
\( 32^{3/5} = (32^{1/5})^3 = 2^3 = 8 \).
Question 3
Points: 1
Simplify: \( (\sqrt{16})^3 \)
Explanation
\( (\sqrt{16})^3 = 4^3 = 64 \).
Question 4
Points: 1
Write as a radical expression: \( y^{2/3} \)
Explanation
Using the rule \( y^{m/n} = \sqrt[n]{y^m} \), the expression \( y^{2/3} \) becomes \( \sqrt[3]{y^2} \).
Squaring both sides gives \( q+1 = 4 \), so \( q = 3 \).
Question 8
Points: 1
What is the first step to solve: \( p = \sqrt{4p+8} - 3 \)?
Explanation
To solve a radical equation, you must first isolate the radical. Adding 3 to both sides results in \( p+3 = \sqrt{4p+8} \).
Question 9
Points: 1
What is the first step to solve: \( (41k-31)^{1/4} = 5 \)?
Explanation
The expression is already isolated. To eliminate the exponent of \( 1/4 \), raise both sides to the power of 4.
Question 10
Points: 1
Solve for x: \( 6x^5 = -192 \)
Explanation
\( x^5 = -192/6 = -32 \). The fifth root of -32 is -2.
Question 11
Points: 1
Simplify. Your answer should contain only positive exponents: \( yx^{1/3} \cdot xy^{3/2} \)
Explanation
Multiply the variables by adding their exponents: \( x^{1/3+1} = x^{4/3} \) and \( y^{1+3/2} = y^{5/2} \).
Question 12
Points: 1
Simplify. Your answer should contain only positive exponents: \( \frac{a^2 b^0}{3a^4} \)
Explanation
Since \( b^0 = 1 \), the expression is \( \frac{a^2}{3a^4} \). Subtracting exponents gives \( \frac{1}{3a^{4-2}} = \frac{1}{3a^2} \).
Question 13
Points: 1
Simplify. Your answer should contain only positive exponents: \( (x^0 y^{1/3})^{3/2} \cdot x^0 \)
Explanation
Since \( x^0 = 1 \), the expression simplifies to \( (y^{1/3})^{3/2} \). Multiply exponents: \( 1/3 \cdot 3/2 = 1/2 \).
Question 14
Points: 1
Find the indicated real \( n^{th} \) root(s) of a: n = 6, a = -729
Explanation
An even root (n=6) of a negative number has no real solution.
Question 15
Points: 1
Find the indicated real \( n^{th} \) root(s) of a: n = 4, a = 256
Explanation
For an even index (n=4) and a positive radicand, there are two real roots: positive and negative. Since \( 4^4 = 256 \), the roots are \( \pm 4 \).
Question 16
Points: 1
Match the equivalent expression: \( 1/(\sqrt[4]{5}) \)
Explanation
The fourth root is \( 5^{1/4} \). Because it is in the denominator, the exponent becomes negative: \( 5^{-1/4} \).
Question 17
Points: 1
Match the equivalent expression: \( (\sqrt[4]{5})^3 \)
Explanation
\( \sqrt[4]{5} \) is \( 5^{1/4} \). Raising this to the 3rd power gives \( (5^{1/4})^3 = 5^{3/4} \).
Result Tracking
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Wrong Answers0
Current Percentage0%
Quiz Completed
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Final Result
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Answered Questions0 / 17
Total Possible Points17
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