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Verify the following: `(a + b + c) (a^2 + b^2 + c^2 – ab – bc – ca) = a^3 + b^3+ c^3 –
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The reciprocal of `(2/5)^-1`
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The multiplicative inverse of `(-5/9)^-99`
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If x be any integer different from zero and m, n be any integers, then `(x^m)^n` is equal
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For a non-zero integer x, `(x^4)^(–3)` is equal
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Express `3^(–5) xx 3^(–4)` as a power of 3 with positive
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Express `16^(–2)` as a power with the base
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Divide 293 by 10,00,000 and express the result in standard
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Find the value of `x^(–3)` if `x = (100)^(1–4) -:
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Find the multiplicative inverse of `(–7)^(–2) -:
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If `53^(x–1) -: 25 = 125`, find the value of
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Some migratory birds travel as much as 15,000 km to escape the extreme climatic conditions at home. Write the distance in metres using scientific
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The number of red blood cells per cubic millimetre of blood is approximately 5.5 million. If the average body contains 5 litres of blood, what is the total number of red cells in the body? Write the standard form. (1 litre = 1,00,000
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`(16 xx 10^2 xx 64)/(2^4 xx
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The cells of a bacteria double itself every hour. How many cells will there be after 8 hours, if initially we start with 1 cell. Express the answer in
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Astronomy The table shows the mass of the planets, the sun and the moon in our solar system. (a) Write the mass of each planet and the Moon in scientific
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Investigating Solar System The table shows the average distance from each planet in our solar system to the sun. (a) Complete the table by expressing the distance from each planet to the Sun in scientific
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While studying her family’s history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex. (a) Make a table and a graph showing the number of ancestors in each of the 12
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Two machines can be hooked together. When something is sent through this hook up, the output from the first machine becomes the input for the second. (a) Which two machines hooked together do the same work a `( xx 10^2)` machine does? Is there more than one arrangement of two machines that will work? (b) Which stretching machine does the same work as two `(xx 2)` machines hooked together?
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For the following repeater machines, how many times the base machine is applied and how much the total stretch is?
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