30 Questions
What is the value of a^0, where a is a non-zero real or imaginary number?
1
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
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^(mn)
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?
x = 0
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?
a^(m-n)
If x and y are rational numbers, what is the condition for x^n + y^n to be divisible by x + y?
n is odd
What is the rationalizing factor for the expression a^(1/3) + a^(-1/3)?
a^(2/3) + a^(-2/3) - 1
If x = a^(1/3) and y = a^(-1/3), what is the value of x^3 + y^3?
a + a^(-1)
What is the value of x - y, given that (x + y)^2 = a^2 + b and xy = (b/4)?
√(a^2 - b)
What is the condition for a + √b to be a square?
a^2 - b is a perfect square
If $a = b \neq 0$, then what can be said about the value of $x$?
$x$ can have any real value
Solve the equation $[f(x)]^\phi(x) = [g(x)]^\phi(x)$, where $\phi(x) \neq 0$.
$\phi(x) = 0$ or $f(x) = g(x)$
Simplify the expression $(x^m)^l \cdot (x^n)^m
$x^{lm + nm}$
Simplify the expression $x^{2/3} \cdot x^{1/3}$
$x$
Solve the equation $x^{2/3} - 2x^{1/3} + 1 = 0
$x = 1$
What is the value of a^(-m) where a is a non-zero real or imaginary number and m is a positive integer?
1/a^m
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?
a and b have the same sign
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^(mn)
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?
x = y
What is the value of (ab)^m where a and b are non-zero real or imaginary numbers and m is a rational number?
a^m b^m
If x and y are rational numbers, what is the condition for x^n - y^n to be divisible by x - y?
n is odd
What is the rationalizing factor for the expression a^(1/n) + a^(-1/n)?
a^(n-1) - a^(n-2)y + ... - y^(n-1)
If x and y are rational numbers, what is the value of x^n + y^n when n is odd?
(x + y)(x^(n-1) + x^(n-2)y + ... + y^(n-1))
What is the value of x^m * x^n when m and n are rational numbers?
x^(m+n)
What is the condition for a + √b to be a square?
b = (a + x)(a - x) for some x
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?
3m + 2n
Solve the equation $x^{3/4} - 2x^{1/4} + 1 = 0$, where x is a real number.
1
What is the value of $x^m + x^{-m}$, where x is a non-zero real number and m is a rational number?
0
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.
x^(2mn)
What is the value of $(x^2)^{1/3} + (x^3)^{1/2}$, where x is a non-zero real number?
x^(1/3) + x^(3/2)
Test your understanding of indices and surds with this quiz. Learn about the definition of indices, laws of indices, and more. Evaluate your knowledge of exponential expressions and rational numbers.
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