Digit : A digit is a symbol used in the representation of a number.

Hundred : Hundred refers to the number 100.

Number : A number $x$ is a mathematical symbol representing a quantity.

Rounding : Rounding is the operation of changing a number to a number that is close to the original number. Rounded numbers are often used to do quick rough calculations for estimation purposes. For example rounding $4549$ to the nearest thousand results in 5000, rounding the same number to the nearest hundred results in 4500. In general one rounds up if the digit after the digit we try to round to is 5 or more, otherwise one rounds down.

Find a one number $a,$ such that $a\cdot a\leq 6$ and $(a+1) \cdot (a+1)> 6.$ Then find a two digit number $b$ with first digit equal to $a$, such that $\frac{b}{10}\cdot \frac{b}{10}\leq 6$ and $\frac{b+1}{10} \cdot \frac{b+1}{10}> 6.$ Finally, check if $\frac{c}{100}\cdot \frac{c}{100}> 6$ for the number $c$ with first two digits equal to $b$ and last digit equal to 5.

Basis : The basis of a vector space is a set of linearly independent vectors, so that every vector of the vector space can be written as a linear combination of the vectors in the basis. For example $\{\left(\begin{smallmatrix}1\\0\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}0\\1\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}0\\0\\1\\\end{smallmatrix}\right)\}$ is a basis of $\mathbb{R}^3.$ In a prove by induction basis refers to the first step in which you have to prove that the result is true for a particular number $n$ (usually $n=0$ or $n=1$.)

Division : Division is the mathematical operation that divides objects equally into groups. More generally $x\div y$ is defined as the number that if multiplied by $y$ equals $x.$

Exponent : In a power $a^x$ the number $x$ is called the exponent of the power.

Half : A Half is the number equal to $\frac{1}{2}=0.5.$

Power : A power is a number of the form $a^b.$ $b$ is called the exponent of the power and $a^b$ is called a power of $a$. For natural numbers $b$ the number $a^b$ is an abbreviation for successively multiplying $a$ by itself $b$ times. For example $2^3=2\cdot 2\cdot 2=8.$ For fractional exponents $b=\frac{p}{q}$ the number $a^{\frac{p}{q}}$ is defined as $\sqrt[q]{a^p}.$ For arbitrary real exponents $b$ the power $a^b$ is defined as the limit of $a^{b_n}$ with rational $b_n$ that converge towards $b.$

Subtraction : Subtraction is the mathematical operation that describes decreasing a number by an amount equal to a second number. The mathematical symbol for subtraction is the minus sign $-.$ The term subtraction is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.

Use $x^a\div x^b=x^{a-b}.$

Basis : The basis of a vector space is a set of linearly independent vectors, so that every vector of the vector space can be written as a linear combination of the vectors in the basis. For example $\{\left(\begin{smallmatrix}1\\0\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}0\\1\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}0\\0\\1\\\end{smallmatrix}\right)\}$ is a basis of $\mathbb{R}^3.$ In a prove by induction basis refers to the first step in which you have to prove that the result is true for a particular number $n$ (usually $n=0$ or $n=1$.)

Division : Division is the mathematical operation that divides objects equally into groups. More generally $x\div y$ is defined as the number that if multiplied by $y$ equals $x.$

Exponent : In a power $a^x$ the number $x$ is called the exponent of the power.

Power : A power is a number of the form $a^b.$ $b$ is called the exponent of the power and $a^b$ is called a power of $a$. For natural numbers $b$ the number $a^b$ is an abbreviation for successively multiplying $a$ by itself $b$ times. For example $2^3=2\cdot 2\cdot 2=8.$ For fractional exponents $b=\frac{p}{q}$ the number $a^{\frac{p}{q}}$ is defined as $\sqrt[q]{a^p}.$ For arbitrary real exponents $b$ the power $a^b$ is defined as the limit of $a^{b_n}$ with rational $b_n$ that converge towards $b.$

Use $a^x\div b^x=(a\div b)^x.$