Quick Review Flashcards - Click to flip and test your knowledge!
Question
In the expression $a^m$, what is the term $a$ called?
Answer
The base.
Question
In the expression $a^m$, what are the three alternative names for the term $m$?
Answer
Power, exponent, or index.
Question
How is the mathematical expression $a^m$ read aloud?
Answer
It is read as '$a$ power $m$' or '$a$ raised to the power $m$'.
Question
Write the product $a \times a \times a \dots$ to $m$ terms using index notation.
Answer
$a^m$
Question
State the 1st Law of Indices (Product Law).
Answer
$a^m \times a^n = a^{m+n}$
Question
State the 2nd Law of Indices (Quotient Law) for the expression $\frac{a^m}{a^n}$.
Answer
$\frac{a^m}{a^n} = a^{m-n}$
Question
State the 3rd Law of Indices (Power Law) for the expression $(a^m)^n$.
Answer
$(a^m)^n = a^{mn}$
Question
Simplify the expression $a^7 \times a^4$.
Answer
$a^{11}$
Question
Simplify the expression $a^3 \times a^{-6}$.
Answer
$a^{-3}$
Question
Simplify the expression $\frac{a^7}{a^4}$.
Answer
$a^3$
Question
Simplify the expression $\frac{a^3}{a^6}$.
Answer
$a^{-3}$
Question
Simplify the expression $(a^3)^4$.
Answer
$a^{12}$
Question
According to the laws for handling indices, what does $(a \times b)^m$ expand to?
Answer
$a^m \times b^m$
Question
According to the laws for handling indices, what does $(\frac{a}{b})^m$ expand to?
Answer
$\frac{a^m}{b^m}$
Question
If $a \ne 0$ and $n$ is a positive integer, express $\sqrt[n]{a}$ in index form.
Answer
$a^{1/n}$
Question
Express the square root $\sqrt{a}$ in index form.
Answer
$a^{1/2}$
Question
Express the cube root $\sqrt[3]{a}$ in index form.
Answer
$a^{1/3}$
Question
Convert the fractional index expression $a^{m/n}$ into radical form.
Answer
$\sqrt[n]{a^m}$
Question
Express $a^{4/5}$ in radical form.
Answer
$\sqrt[5]{a^4}$
Question
Express $5^{2/3}$ in radical form.
Answer
$\sqrt[3]{5^2}$
Question
For any non-zero number $a$, what is the equivalent of $a^{-n}$ with a positive index?
Answer
$\frac{1}{a^n}$
Question
For any non-zero number $a$, what is the equivalent of $a^n$ using a negative index?
Answer
$\frac{1}{a^{-n}}$
Question
What is the value of any non-zero number raised to the power zero ($a^0$)?
Answer
1 (or unity).
Question
Rule: If $m$ is an even number, what is the result of $(-a)^m$?
Answer
$a^m$
Question
Rule: If $m$ is an odd number, what is the result of $(-a)^m$?
Answer
$-a^m$
Question
Evaluate the numerical value of $(-2)^4$.
Answer
$16$ (or $2^4$)
Question
Evaluate the numerical value of $(-2)^5$.
Answer
$-32$ (or $-2^5$)
Question
Evaluate $27^{-1/3}$.
Answer
$\frac{1}{3}$
Question
Evaluate $9^{3/2}$.
Answer
$27$
Question
Simplify $(\frac{1}{81})^{-1/2}$.
Answer
$9$ (or $81^{1/2}$)
Question
In the process of solving exponential equations, if $a^x = a^y$, what can be concluded about $x$ and $y$?
Answer
$x = y$
Question
When simplifying an expression like $\frac{3^{a+2} - 3^{a+1}}{4 \times 3^a - 3^a}$, what is the first step to isolate $3^a$?
Answer
Factor out $3^a$ from the numerator and the denominator.
Question
Simplify the expression $(a^{m-n})^{m+n} \cdot (a^{n-l})^{n+l} \cdot (a^{l-m})^{l+m}$.
Answer
1
Question
To solve the equation $9 \times 3^x = (27)^{2x-5}$, into what common base should both sides be converted?
Answer
Base 3.
Question
When solving $2^{2x+3} - 9 \times 2^x + 1 = 0$, what substitution is recommended to simplify the equation into a quadratic?
Answer
Substitute $2^x = y$.
Question
Evaluate the value of $(2 \times 3)^5$.
Answer
$2^5 \times 3^5$
Question
Convert $\sqrt[3]{a^5}$ into index form.
Answer
$a^{5/3}$
Question
Convert $\sqrt{10}$ into index form.
Answer
$10^{1/2}$
Question
If $1176 = 2^p \cdot 3^q \cdot 7^r$, what are the values of $p, q$, and $r$ after prime factorisation?
Answer
$p = 3, q = 1, r = 2$
Question
Evaluate $32^{0.8}$ by converting the decimal index to a fraction.
Answer
$16$
Question
What is the value of $(0.8)^{-1}$ as a fraction?
Answer
$\frac{5}{4}$ (or $1.25$)
Question
Simplify the quotient $(\frac{2}{3})^{-2}$.
Answer
$\frac{9}{4}$
Question
Simplify $a^n \cdot a^{-n}$.
Answer
1
Question
How is the expression $(\sqrt{x})^y$ represented in index form?
Answer
$x^{y/2}$
Question
In an exponential equation, if the bases on both sides are equal, what must be done with the exponents?
Answer
The exponents must be equated.
Question
Solve for $x$: $2^{2x+1} = 8$.
Answer
$x = 1$
Question
Solve for $x$: $4^{2x} = \frac{1}{32}$.
Answer
$x = -1.25$ (or $-\frac{5}{4}$)
Question
What does the expression $x^{a-b} \cdot x^{b-c} \cdot x^{c-a}$ simplify to?
Answer
1
Question
Simplify $(\frac{2a^2}{b^3})^4$.
Answer
$\frac{16a^8}{b^{12}}$
Question
What is the value of $(20^0 - 18^0) \times 7^0$?
Answer
0
Question
Simplify $(a+b)^{-1} \cdot (a^{-1} + b^{-1})$.
Answer
$\frac{1}{ab}$
Question
If $x^a = y, y^b = z$, and $z^c = x$, what is the value of $abc$?
Answer
1
Question
Simplify $(\frac{x^a}{x^b})^{a+b} \cdot (\frac{x^b}{x^c})^{b+c} \cdot (\frac{x^c}{x^a})^{c+a}$.
Answer
1
Question
Determine the value of $x$ if $8^{2x+5} = 1$.
Answer
$x = -2.5$ (or $-\frac{5}{2}$)
Question
Simplify $2^3 \times (243)^{-2/3} \times 9^{-1/3}$ by converting to base 3.
Answer
$\frac{8}{27}$
Question
Convert the radical expression $\sqrt[n]{x^m}$ into index form.
Answer
$x^{m/n}$
Question
Evaluate $5^{-4} \times (125)^{5/3} \div (25)^{-1/2}$.
Answer
25
Question
Simplify $(3x^2)^{-3} \times (x^9)^{2/3}$.
Answer
$\frac{1}{27}$
Question
If $a^x = b^y = c^z$ and $b^2 = ac$, what is the relationship between $x, y$, and $z$?
Answer
$\frac{2}{y} = \frac{1}{x} + \frac{1}{z}$
Question
Evaluate $(0.01)^{1/2}$.
Answer
0.1