MAST Grade 8 Exponent Rules and Scientific Notation Practice

Exponent Rules and Scientific Notation skills

Apply rules of exponents to produce equivalent expressions.

Use scientific notation to solve problems.

Standards: 8.EE.1, 8.EE.3, 8.EE.4

Standards basis

Montana PK-12 Mathematics Content Standards / Common Core State Standards for Mathematics (CCSS-M)-aligned Montana standards — Montana

How the MAST reports it

Montana’s MAST is a state-specific through-year assessment built by New Meridian and aligned to Montana’s academic content standards, not a Smarter Balanced-style claims/targets framework. The math blueprints organize content into grade-level strands/testlets that map directly to CCSS-M-derived Montana standards.

Blueprint & weighting

The blueprint publishes a through-year design of 12 strands/testlets per grade, with 1 strand per testlet, 2 reporting attributes per strand, and 9–13 items per testlet. It also specifies approximate item-type and DOK distributions, but does not publish percentage weighting by domain in the captured blueprint text.

Official sources

Montana OPI MontCAS
Montana OPI - MasteryGuide Mathematics Assessment Specifications and Blueprints
Montana OPI - Montana MAST Math Testlets

8 free questions · 0/0 correct

Practice playeasy

Rewrite $a^{-2}$ with a positive exponent.

The Negative Exponent Property says that a nonzero base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, written $a^{-n} = \dfrac{1}{a^{n}}\textsf{.}$ Applying the property, $a^{-2} = \dfrac{1}{a^{2}}\textsf{.}$

Practice playhard

Let $f(t) = e^{3t}$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(5)$ ?

Substitute $t = 5$ : $f(5) = e^{15}$ . Since $e^{15} \approx 3{,}269{,}017$ , $f(5) \approx 3 \times 10^{6}$ .

Practice playeasy

Write $4500$ as $a \times 10^n$ where $1 \le a < 10$ . What is $n$ ?

$4500 = 4.5 \times 10^3$ , so $n = 3$ .

Practice playmedium

$(1.5 \times 10^{4})(8 \times 10^{3})$ equals

Multiply coefficients and add exponents: $1.5 \cdot 8 = 12$ and $4+3=7$ , giving $12 \times 10^{7}$ . Rewrite as $1.2 \times 10^{1} \times 10^{7}=1.2 \times 10^{8}\textsf{.}$

Practice playeasy

$(3 \cdot 7)^{4} = 3^{a} \cdot 7^{a}\textsf{.}$ What is $a\textsf{?}$

The Power of a Product Property says that a product raised to a power equals each factor raised to that power, written $(ab)^{n} = a^{n} \cdot b^{n}\textsf{.}$ Here $(3 \cdot 7)^{4} = 3^{4} \cdot 7^{4}$ , so $a = 4\textsf{.}$

Practice playmedium

Let $f(t) = 8e^{3t} + 50$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(2)$ ?

Substitute $t = 2$ : $f(2) = 8e^{6} + 50$ . Since $e^{6} \approx 403.4$ , $f(2) \approx 8(403.4) + 50 = 3{,}277 \approx 3 \times 10^{3}$ .

Practice playeasy

$(2 \times 10^3)(3 \times 10^4) = 6 \times 10^n$ . What is $n$ ?

Multiply coefficients ( $2 \cdot 3 = 6$ ) and add exponents: $3 + 4 = 7$ , so $n = 7$ .

Practice playmedium

What is $(5 \times 10^{-3})(4 \times 10^{-2})$ in scientific notation?

Multiply coefficients and add exponents: $5 \cdot 4 = 20$ and $-3+(-2)=-5$ , giving $20 \times 10^{-5}$ . Rewrite $20=2 \times 10^{1}$ , so $2 \times 10^{1} \times 10^{-5}=2 \times 10^{-4}\textsf{.}$