Express each of the following as a rational number of the form p/q, where p and q are integers and q ≠ 0:
(i) 2-3
(ii) (-4)-2
(iii) 1/(3)-2
(iv) (1/2)-5
(v) (2/3)-2
Find the values of each of the following:
(i) 3-1 + 4-1
(ii) (30 + 4-1) × 22
(iii) (3-1 + 4-1 + 5-1)0
(iv) ((1/3)-1 – (1/4)-1)-1
(i) (1/2)-1 + (1/3)-1 + (1/4)-1
(ii) (1/2)-2 + (1/3)-2 + (1/4)-2
(iii) (2-1 × 4-1) ÷ 2-2
(iv) (5-1 × 2-1) ÷ 6-1
Simplify:
(i) (4-1 × 3-1)2
(ii) (5-1 ÷ 6-1)3
(iii) (2-1 + 3-1)-1
(iv) (3-1 × 4-1)-1 × 5-1
(i) (32 + 22) × (1/2)3
(ii) (32 – 22) × (2/3)-3
(iii) ((1/3)-3 – (1/2)-3) ÷ (1/4)-3
(iv) (22 + 32 – 42) ÷ (3/2)2
By what number should 5-1 be multiplied so that the product may be equal to (-7)- 1?
By what number should (1/2)-1 be multiplied so that the product may be equal to (-4/7)-1?
By what number should (-15)-1 be divided so that the quotient may be equal to (- 5)-1?
Write each of the following in exponential form:
(i) (3/2)^{-1} × (3/2)^{-1} × (3/2)^{-1} × (3/2)^{-1}
(ii) (2/5)^{-2} × (2/5)^{-2} × (2/5)^{-2}
Evaluate:
(i) 5-2
(ii) (-3)-2
(iii) (1/3)-4
(iv) (-1/2)-1
Express each of the following as a rational number in the form p/q:
(i) 6-1
(ii) (-7)-1
(iii) (1/4)-1
(iv) (-4)-1 × (-3/2)-1
(v) (3/5)-1 × (5/2)-1
(i) (4-1 × 3-1) 2
(ii) (5-1 ÷ 6-1) 3
(iii) (2-1 + 3-1) -1
(iv) (3-1 × 4-1) -1 × 5-1
(v) (4-1 – 5-1) ÷ 3-1
Express each of the following rational numbers with a negative exponent:
(i) (1/4)3
(ii) 35
(iii) (3/5)4
(iv) ((3/2)4)-3
(v) ((7/3)4)-3
Express each of the following rational numbers with a positive exponent:
(i) (3/4)-2
(ii) (5/4)-3
(iii) 43 × 4-9
(iv) ((4/3)-3)-4
(v) ((3/2)4)-2
(i) ((1/3)-3 – (1/2)-3) ÷ (1/4)-3
(iii) ((1/2)-1 × (-4)-1)-1
(iv) (((-1/4)2)-2)-1
(v) ((2/3)2)3 × (1/3)-4 × 3-1 × 6-1
By what number should (5/3)-2 be multiplied so that the product may be (7/3)-1?
Find x, if
(i) (1/4)-4 × (1/4)-8 = (1/4)-4x
(ii) (-1/2)-19 ÷ (-1/2)8 = (-1/2)-2x+1
(iii) (3/2)-3 × (3/2)5 = (3/2)2x+1
(iv) (2/5)-3 × (2/5)15 = (2/5)2+3x
(v) (5/4)-x ÷ (5/4)-4 = (5/4)5
(vi) (8/3)2x+1 × (8/3)5 = (8/3) x+2
(i) If x= (3/2)2 × (2/3)-4 , find the value of x-2. (ii) If x = (4/5)-2 ÷ (1/4)2 , find the value of x-1.
Find the value of x for which 52x ÷ 5-3 = 55
Express the following numbers in standard form:
(i) 6020000000000000
(ii) 0.00000000000942
(iii) 0.00000000085
(iv) ^{846\times10^7}
(v) 3759\times10^{-4}
(vi) 0.00072984
(vii) 0.000437\times10^4
(viii) 4 ÷ 100000
Write the following numbers in the usual form:
(i) 4.83\times10^7
(ii) 3.02\times10^{-6}
(iii) 4.5\times10^4
(iv) 3\times10^{-8}
(v)1.0001\times10^9
(vi) 5.8 × 10^2
(vii) 3.61492 × 10^6
(vii) 3.25 × 10^{-7}
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