\(9^2=3^4\) and \(27^{-1}=3^{-3}\), so the value is \(3^{-2+4-(-3)}=3^5=243\). In exams, be careful while subtracting a negative exponent.
Step 2
Why this answer is correct
The correct answer is A. (,243,). \(9^2=3^4\) and \(27^{-1}=3^{-3}\), so the value is \(3^{-2+4-(-3)}=3^5=243\). In exams, be careful while subtracting a negative exponent.
Step 3
Exam Tip
\(9^2=3^4\) और \(27^{-1}=3^{-3}\), इसलिए मान \(3^{-2+4-(-3)}=3^5=243\) है। परीक्षा में negative exponent घटाते समय सावधान रहें।
Since \(81=3^4\), we get (2x-1=4) and \(x=\dfrac{5}{2}\). In exams, equate exponents when the bases are the same.
Step 2
Why this answer is correct
The correct answer is A. \(,\dfrac{5}{2},\). Since \(81=3^4\), we get (2x-1=4) and \(x=\dfrac{5}{2}\). In exams, equate exponents when the bases are the same.
Step 3
Exam Tip
क्योंकि \(81=3^4\), इसलिए (2x-1=4) और \(x=\dfrac{5}{2}\)। परीक्षा में समान आधार होने पर घातांकों को बराबर करें।
Since \(4^{x+1}=2^{2x+2}\) and \(128=2^7\), we get (2x+2=7) and \(x=\dfrac{5}{2}\). In exams, write both sides with the same base.
Step 2
Why this answer is correct
The correct answer is A. \(,\dfrac{5}{2},\). Since \(4^{x+1}=2^{2x+2}\) and \(128=2^7\), we get (2x+2=7) and \(x=\dfrac{5}{2}\). In exams, write both sides with the same base.
Step 3
Exam Tip
क्योंकि \(4^{x+1}=2^{2x+2}\) और \(128=2^7\), इसलिए (2x+2=7) तथा \(x=\dfrac{5}{2}\)। परीक्षा में दोनों पक्षों को समान आधार में लिखें।
Here \(9^{-1}=3^{-2}\) and \(27^{-1}=3^{-3}\), so the value is \(3^{4-2-(-3)}=3^5=243\). In exams, convert all terms to the same base.
Step 2
Why this answer is correct
The correct answer is A. (,243,). Here \(9^{-1}=3^{-2}\) and \(27^{-1}=3^{-3}\), so the value is \(3^{4-2-(-3)}=3^5=243\). In exams, convert all terms to the same base.
Step 3
Exam Tip
यहां \(9^{-1}=3^{-2}\) और \(27^{-1}=3^{-3}\), इसलिए मान \(3^{4-2-(-3)}=3^5=243\) है। परीक्षा में सभी पदों को समान आधार में बदलें।
The numerator is \(2^{10}+2^{10}=2\times 2^{10}=2^{11}\), so \(\dfrac{2^{11}}{2^9}=2^2=4\). In exams, first combine like terms and then apply exponent laws.
Step 2
Why this answer is correct
The correct answer is A. (,4,). The numerator is \(2^{10}+2^{10}=2\times 2^{10}=2^{11}\), so \(\dfrac{2^{11}}{2^9}=2^2=4\). In exams, first combine like terms and then apply exponent laws.
Step 3
Exam Tip
ऊपर \(2^{10}+2^{10}=2\times 2^{10}=2^{11}\), इसलिए \(\dfrac{2^{11}}{2^9}=2^2=4\)। परीक्षा में पहले समान terms को जोड़ें फिर घात नियम लगाएं।
The numerator gives \(a^m \times a^{2m}=a^{3m}\), and then \(\dfrac{a^{3m}}{a^{3m-2}}=a^2\). In exams, subtract exponents during division.
Step 2
Why this answer is correct
The correct answer is A. \(,a^2,\). The numerator gives \(a^m \times a^{2m}=a^{3m}\), and then \(\dfrac{a^{3m}}{a^{3m-2}}=a^2\). In exams, subtract exponents during division.
Step 3
Exam Tip
ऊपर \(a^m \times a^{2m}=a^{3m}\) और फिर \(\dfrac{a^{3m}}{a^{3m-2}}=a^2\) होगा। परीक्षा में भाग करते समय घातांक घटाएं।
Here \(8=2^3\) and (42=\(2^2\)2=24), so \(\dfrac{2^5 \times 2^3}{2^4}=2^4=16\). In exams, converting numbers to the same base is useful.
Step 2
Why this answer is correct
The correct answer is A. (,16,). Here \(8=2^3\) and (42=\(2^2\)2=24), so \(\dfrac{2^5 \times 2^3}{2^4}=2^4=16\). In exams, converting numbers to the same base is useful.
Step 3
Exam Tip
यहां \(8=2^3\) और (42=\(2^2\)2=24), इसलिए \(\dfrac{2^5 \times 2^3}{2^4}=2^4=16\)। परीक्षा में सभी संख्याओं को समान आधार में बदलना उपयोगी होता है।
