EXERCISE 1.6
EVIDYARTHIQ 1 Ex 1.6, Page No 26, Number Systems, Class 9th Maths
MKRLaws of Powers and Exponents
Class - 9th, Ex - 1.6, Q 1 ( NUMBER SYSTEM ) CBSE NCERT
Page No 26:
Question 1:
Find:(i) 64^{\frac{1}{2}}
(ii) 32^{\frac{1}{5}}
(iii) 125^{\frac{1}{3}}
Answer:
(i) 64^{\frac{1}{2}}=\left(2^{6}\right)^{\frac{1}{2}}=2^{6 \times \frac{1}{2}} \left[\left(a^{m}\right)^{n}=a^{m n}\right]
=2^{3}=8
(ii) 32^{\frac{1}{5}}=\left(2^{5}\right)^{\frac{1}{5}}
=(2)^{5 \times \frac{1}{5}} \left[\left(a^{m}\right)^{n}=a^{m n}\right]
=2^{1}=2
(iii) (125)^{\frac{1}{3}}=\left(5^{3}\right)^{\frac{1}{3}}
=5^{3 \times \frac{1}{3}} \left[\left(a^{m}\right)^{n}=a^{m n}\right]
=5^{1}=5
EVIDYARTHI
Q 2, Ex 1.6, Page No 26, Number Systems, CBSE Maths Class 9th
MKR
Class - 9th, Ex - 1.6, Q 2 ( NUMBER SYSTEM ) CBSE NCERT
Question 2:
Q2. Find:(i) 9^{\frac{3}{2}}
(ii) 32^{\frac{2}{5}}
(iii) 16^{\frac{3}{4}}
(iv) 125^{\frac{-1}{3}}
Answer:
(i) 9^{\frac{3}{2}}=\left(3^{2}\right)^{\frac{3}{2}}=3^{2 \times \frac{3}{2}} \left[\left(a^{m}\right)^{n}=a^{m n}\right]
=3^{3}=27
(ii) (32)^{\frac{2}{5}}=\left(2^{5}\right)^{\frac{2}{5}}
=2^{5 \times \frac{2}{5}} \left[\left(a^{m}\right)^{n}=a^{m n}\right]
=2^{2}=4
(iii) (16)^{\frac{3}{4}}=\left(2^{4}\right)^{\frac{3}{4}}
=2^{4 \times \frac{3}{4}} \left[\left(a^{m}\right)^{n}=a^{m n}\right]
=2^{3}=8
(iv) (125)^{\frac{-1}{3}}=\frac{1}{(125)^{\frac{1}{3}}} \left[a^{-m}=\frac{1}{a^{m}}\right]
=\frac{1}{\left(5^{3}\right)^{\frac{1}{3}}}
=\frac{1}{5^{3 \times \frac{1}{3}}} \left[\left(a^{m}\right)^{n}=a^{m n}\right]
=\frac{1}{5}
EVIDYARTHI
Q 3, Ex 1.6, Page No 26, Number Systems, Class 9th Mathematics
MKR
Class - 9th, Ex - 1.6, Q 3 ( NUMBER SYSTEM ) CBSE NCERT
Question 3:
Simplify:(i) 2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}}
(ii) \left(\frac{1}{3^{3}}\right)^{7}
(iii) \frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}
(iv) 7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}
Answer:
(i) 2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}}=2^{\frac{2}{3}+1} \left[a^{m} \cdot a^{n}=a^{m+n}\right]=2^{\frac{10+3}{15}}=2^{\frac{13}{15}}
(ii) \left(\frac{1}{3^{3}}\right)^{7}=\frac{1}{3^{3 \times 7}} \left[\left(a^{m}\right)^{n}=a^{m n}\right]
=\frac{1}{3^{21}}
=3^{-21} \left[\frac{1}{a^{m}}=a^{-m}\right]
(iii) \frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}=11^{\frac{1}{2}-\frac{1}{4}} \left[\frac{a^{m}}{a^{n}}=a^{m-n}\right]
=11^{\frac{2-1}{4}}=11^{\frac{1}{4}}
(iv) 7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}=(7 \times 8)^{\frac{1}{2}} \left[a^{m} \cdot b^{m}=(a b)^{m}\right]
=(56)^{\frac{1}{2}}
0 comments:
Post a Comment