Fractional and Negative Indices
-
Non-calculator 1 mark
Write down the value of \(12^{0}\)
-
Non-calculator 2 marks(a)
Write down the value of \(7^{-1 }\)
(b)Find the value of \(4^{-2 }\)
-
Non-calculator 2 marks(a)
\(a^{ 6 } \times a^n = a^{ 15 }\)
Work out the value of \(n\).
(b)\(a^{ 8 } \div a^n = a^{ 3 }\)
Work out the value of \(n\).
-
Non-calculator 2 marks
Express \(\frac{ 7^{ 5 } \times 7^{ 7 } }{ 7^{ 14 } }\) as a single power of 7, in the form \(7^n\) where \(n\) is an integer.
-
Non-calculator Higher4 marks(a)
\(n^{\frac{1}{2}} = 8\)
Find the value of \(n\).
(b)\(m^{\frac{1}{3}} = 6\)
Find the value of \(m\).
-
Non-calculator Higher1 mark
Hafsa says that \(\frac{1}{ 2 }\) of 36 is 18, so \(36^{\frac{1}{ 2 }} = 18\).
Hafsa is wrong. Work out the correct value of \(36^{\frac{1}{ 2 }}\).
-
Non-calculator Higher5 marks(a)
Find the value of \(16^{\frac{1}{ 4 } }\)
(b)Find the value of \(256^{\frac{ 3 }{ 4 } }\)
(c)Find the value of \(25^{\frac{3}{2} }\)
-
Non-calculator Higher5 marks(a)
Write \(\sqrt{ p }\) as a power of \(p\)
(b)Write \(\frac{ 8 }{ p^{ 5 } }\) in the form \(ap^n\)
(c)Write \(p\sqrt{ p }\) as a power of \(p\)
-
Non-calculator 3 marks
Write \(4 \div (32^{ n })^{3}\) as a power of 2.
Give your answer in terms of \(n\).
-
Non-calculator Higher4 marks(a)
Work out \(9^{-\frac{1}{2} }\)
Give your answer as a fraction.
(b)Work out \(27^{-\frac{ 2 }{ 3 } }\)
Give your answer as a fraction.
- \(1\)
-
(a) \(\frac{1}{ 7 }\)
(b) \(\frac{1}{ 16 }\) -
(a) \(9\)
(b) \(5\) - \(7^{ -2 }\)
-
(a) \(64\)
(b) \(216\) - \(6\)
-
(a) \(2\)
(b) \(64\)
(c) \(125\) -
(a) \(p^{\frac{1}{2} }\)
(b) \(8p^{-5 }\)
(c) \(p^{\frac{3}{2} }\) - \(2^{ 2 - 15n }\)
-
(a) \(\frac{1}{ 3 }\)
(b) \(\frac{1}{ 9 }\)
Takes a couple of seconds the first time a sheet is made.