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Indices and Surds
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Indices and Surds

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Questions and Answers

What is the value of a^0, where a is a non-zero real or imaginary number?

  • 0
  • a
  • Undefined
  • 1 (correct)
  • What is the condition for a^m = a^n, where a is a non-zero real or imaginary number and m and n are rational numbers?

  • m > n
  • m = n (correct)
  • m < n
  • m ≠ n
  • What is the value of (a^m)^n, where a is a non-zero real or imaginary number and m and n are rational numbers?

  • a^(m-n)
  • a^(m+n)
  • a^(mn) (correct)
  • a^(m/n)
  • What is the condition for a^x = b^x, where a and b are non-zero real or imaginary numbers and x is a rational number?

    <p>x = 0</p> Signup and view all the answers

    What is the value of a^m/a^n, where a is a non-zero real or imaginary number and m and n are rational numbers?

    <p>a^(m-n)</p> Signup and view all the answers

    If x and y are rational numbers, what is the condition for x^n + y^n to be divisible by x + y?

    <p>n is odd</p> Signup and view all the answers

    What is the rationalizing factor for the expression a^(1/3) + a^(-1/3)?

    <p>a^(2/3) + a^(-2/3) - 1</p> Signup and view all the answers

    If x = a^(1/3) and y = a^(-1/3), what is the value of x^3 + y^3?

    <p>a + a^(-1)</p> Signup and view all the answers

    What is the value of x - y, given that (x + y)^2 = a^2 + b and xy = (b/4)?

    <p>√(a^2 - b)</p> Signup and view all the answers

    What is the condition for a + √b to be a square?

    <p>a^2 - b is a perfect square</p> Signup and view all the answers

    If $a = b \neq 0$, then what can be said about the value of $x$?

    <p>$x$ can have any real value</p> Signup and view all the answers

    Solve the equation $[f(x)]^\phi(x) = [g(x)]^\phi(x)$, where $\phi(x) \neq 0$.

    <p>$\phi(x) = 0$ or $f(x) = g(x)$</p> Signup and view all the answers

    Simplify the expression $(x^m)^l \cdot (x^n)^m

    <p>$x^{lm + nm}$</p> Signup and view all the answers

    Simplify the expression $x^{2/3} \cdot x^{1/3}$

    <p>$x$</p> Signup and view all the answers

    Solve the equation $x^{2/3} - 2x^{1/3} + 1 = 0

    <p>$x = 1$</p> Signup and view all the answers

    What is the value of a^(-m) where a is a non-zero real or imaginary number and m is a positive integer?

    <p>1/a^m</p> Signup and view all the answers

    If a^x = b^x where a and b are non-zero real or imaginary numbers and x is a rational number, what can be said about a and b?

    <p>a and b have the same sign</p> Signup and view all the answers

    What is the value of (a^m)^n where a is a non-zero real or imaginary number and m and n are rational numbers?

    <p>a^(mn)</p> Signup and view all the answers

    What is the condition for a^x = a^y where a is a non-zero real or imaginary number and x and y are rational numbers?

    <p>x = y</p> Signup and view all the answers

    What is the value of (ab)^m where a and b are non-zero real or imaginary numbers and m is a rational number?

    <p>a^m b^m</p> Signup and view all the answers

    If x and y are rational numbers, what is the condition for x^n - y^n to be divisible by x - y?

    <p>n is odd</p> Signup and view all the answers

    What is the rationalizing factor for the expression a^(1/n) + a^(-1/n)?

    <p>a^(n-1) - a^(n-2)y + ... - y^(n-1)</p> Signup and view all the answers

    If x and y are rational numbers, what is the value of x^n + y^n when n is odd?

    <p>(x + y)(x^(n-1) + x^(n-2)y + ... + y^(n-1))</p> Signup and view all the answers

    What is the value of x^m * x^n when m and n are rational numbers?

    <p>x^(m+n)</p> Signup and view all the answers

    What is the condition for a + √b to be a square?

    <p>b = (a + x)(a - x) for some x</p> Signup and view all the answers

    What is the value of x in the equation $(x^m)^l \cdot (x^n)^m = x^{3m + 2n}$, where m, n, and l are integers?

    <p>3m + 2n</p> Signup and view all the answers

    Solve the equation $x^{3/4} - 2x^{1/4} + 1 = 0$, where x is a real number.

    <p>1</p> Signup and view all the answers

    What is the value of $x^m + x^{-m}$, where x is a non-zero real number and m is a rational number?

    <p>0</p> Signup and view all the answers

    Simplify the expression $(x^m)^n \cdot (x^n)^m$, where x is a non-zero real number and m and n are rational numbers.

    <p>x^(2mn)</p> Signup and view all the answers

    What is the value of $(x^2)^{1/3} + (x^3)^{1/2}$, where x is a non-zero real number?

    <p>x^(1/3) + x^(3/2)</p> Signup and view all the answers

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