CRE 1 - Indices | Algebra - Surds & Indices

$3^{\frac{1}{2}}\times 3^{\frac{3}{2}}\times 3^{\frac{5}{2}}\times 3^{\frac{7}{2}}\times 3^{\frac{9}{2}}\times 3^{\frac{11}{2}}$ = 27^x. Find x.

• (a)

  6

• (b)

  4

• (c)

  8

• (d)

  10

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Find x, if $3^{x^x}$ = 81

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Simplify: ${\left[{\left(\frac{2}{3}\right)}^2\right]}^3\times {\left(\frac{1}{3}\right)}^{-4}\times 3^{-1}\times \frac{1}{6}$

• (a)

  27/48

• (b)

  32/81

• (c)

  9/16

• (d)

  16/27

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Given that 10^0.5 = x, 10^0.7 = y and x^z = y², then the value of z is close to:

• (a)

  1.45

• (b)

  1.88

• (c)

  2.8

• (d)

  3.7

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Find the value of x, 2^5x-1 = $2^{2^{4^{1^{5^{2^{9^2}}}}}}$

• (a)

  -7/5

• (b)

  2

• (c)

  5

• (d)

  17/5

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Find x: 15^3x+3 = 225^x-1

• (a)

  -7

• (b)

  5

• (c)

  -3

• (d)

  -5

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If 2^a3^b = 864. Find a + b if a and b are integers.

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Solve for integral value x, if ${\left(5\sqrt{7}\right)}^{5\mathrm{x}-4}$ = ${\left(35\right)}^3{\left(25\right)}^{3/2}$

• (a)

  2

• (b)

  7/2

• (c)

  5/4

• (d)

  3

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Simplify: ${\left(\frac{{\mathrm{a}}^{\mathrm{x}+\mathrm{y}}}{a^y}\right)}^{\frac{x}{yz}}\times {\left(\frac{{\mathrm{a}}^{\mathrm{y}+\mathrm{z}}}{a^z}\right)}^{\frac{y}{zx}}\times {\left(\frac{{\mathrm{a}}^{\mathrm{z}+\mathrm{x}}}{a^x}\right)}^{\frac{z}{yx}}$ if x + y + z = 0.

• (a)

  1

• (b)

  a³

• (c)

  0

• (d)

  a

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Which of the following is correct?

• (a)

  2³⁰⁰ > 3²⁰⁰

• (b)

  2³⁰⁰ < 3²⁰⁰

• (c)

  2³⁰⁰ = 3²⁰⁰

• (d)

  More than 1 of the above

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Arrange in decreasing order: 3^1/2, 4^1/5, 5^1/4

• (a)

  3^1/2 > 4^1/5 > 5^1/4

• (b)

  5^1/4 > 3^1/2 > 4^1/5

• (c)

  4^1/5 > 5^1/4 > 3^1/2

• (d)

  3^1/2 > 5^1/4 > 4^1/5

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If $\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}\dots \dots \mathrm{\infty }}}}={11}^{\mathrm{x}}$, what is the value of $\sqrt[\mathrm{x}]{\mathrm{x}}$?

• (a)

  11

• (b)

  1

• (c)

  √11

• (d)

  11^1/x

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Find the value of $\sqrt{2+\sqrt{2+\sqrt{2+\mathrm{ }\dots \dots \mathrm{\infty }}}}$

• (a)

  2

• (b)

  -1

• (c)

  3

• (d)

  More than one of the above

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If 5^x = (0.125)^y = 10^3z, then what is the relation between x, y and z, given that they are non-zero real numbers?

• (a)

  $\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{y}}+\frac{1}{\mathrm{z}}=1$

• (b)

  $\mathrm{ }\frac{3}{\mathrm{x}}=\frac{1}{\mathrm{y}}+\frac{1}{\mathrm{z}}$

• (c)

  $\frac{1}{\mathrm{z}}-\frac{1}{\mathrm{y}}-\frac{1}{\mathrm{x}}=1$

• (d)

  xyz = 1

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What is the value of z in terms of x and y, if 3^x = 2^y = 6^z, and x, y and z are non-zero?

• (a)

  $\mathrm{z}=\frac{\mathrm{x}+\mathrm{y}}{4\mathrm{xy}}$

• (b)

  $\mathrm{z}=\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}$

• (c)

  $\mathrm{z}=\frac{\mathrm{x}+\mathrm{y}}{2}$

• (d)

  $\mathrm{z}=\frac{{\mathrm{x}}^2+{\mathrm{y}}^2}{\mathrm{xy}}$

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If p² + q² + r² = 1 what is the value of $\left(\sqrt[-\mathrm{pq}]{{\mathrm{a}}^{\mathrm{r}}}\right)\times \left(\sqrt[-\mathrm{qr}]{{\mathrm{a}}^{\mathrm{p}}}\right)\times \left(\sqrt[-\mathrm{pr}]{{\mathrm{a}}^{\mathrm{q}}}\right)?$?

• (a)

  a^pqr

• (b)

  a^1/pqr

• (c)

  1/a^pqr

• (d)

  a^-1/pqr

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