ACC Math 7 Practice Test: Integer Exponents

Vocabulary and mathematical rules derived from the ACC Math 7 Practice Test on Concept Category 9: Integer Exponents and Scientific Notation.

Integer Exponents

The mathematical concept category focusing on operations with exponents, including product, quotient, and power rules involving integers.

Scientific Notation

A way of writing numbers as the product of a decimal between 1 and 10 and a power of 10, such as writing $0.0000643$ as $6.43 \times 10^{-5}$.

Standard Notation

The conventional way of writing numbers using digits, such as expressing $8 \times 10^8$ as $800,000,000$.

Negative Exponent Rule

A property stating that $x^{-1} = \frac{1}{x}$, which allows terms with negative exponents like $y^{-4}$ to be rewritten in the denominator of a fraction.

Product of Powers Rule

A rule used to simplify expressions like $-3xy^{-4} \cdot 2x^5y$ by adding the exponents of terms with the same base.

Quotient of Powers Rule

A method to simplify fractions like $\frac{2x^3}{4x^{-2}y^3}$ by subtracting the exponents of terms with the same base in the numerator and denominator.

Power of a Power Rule

A rule for simplifying expressions such as $(3x^2y^{-5})^{-2}$ by multiplying the inner exponents by the outer exponent.

Power of a Product Rule

A process where every factor inside the parentheses is raised to the external power, such as in $(9xy)^2$.

Magnification Calculation

Determining the actual size of an object, like a speck of dust, by dividing the image size ($1.2 \times 10^2\,mm$) by the magnification factor ($5 \times 10^2$).

Population per square mile

A measure of population density calculated by dividing the total population (e.g., $3.84 \times 10^6$) by the total area in square miles.