Expressions & Equations

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8th Grade Math › Expressions & Equations

Questions 1 - 10

Convert the given value to scientific notation.

Explanation

Scientific notation is used to simplify exceptionally complex numbers and to quickly present the number of significant figures in a given value. The value is converted to an exponent form using base ten, such that only a single-digit term with any given number of decimal places is used to represent the significant figures of the given value. Non-significant zeroes can be omitted from the leading term, and represented only in the base ten exponent.

The given number has five significant figures (100.43), so there will be five digits multiplied by the base ten term.

To generate the single-digit leading term the decimal must be placed after the 1 (1.0043). Then count the digits to the right of the decimal to determine the change in decimal placement (the decimal moves past the two zeroes). Our ten will be raised to the power of two because there are two digits to the right of the final decimal placement.

Our final answer is

Convert the given value to scientific notation.

Explanation

The given number has five significant figures (100.43), so there will be five digits multiplied by the base ten term.

Our final answer is

Evaluate: $\dpi{100} (3^{3})^{2}$

$\dpi{100} 3^{6}$

$\dpi{100} 3^{5}$

$\dpi{100} 243$

$\dpi{100} 729$

Explanation

A power raised to a power indicates that you multiply the two powers.

$\dpi{100} (3^{3})^{2}=3^{3\cdot 2}=3^{6}$

Evaluate: $\dpi{100} (3^{3})^{2}$

$\dpi{100} 3^{6}$

$\dpi{100} 3^{5}$

$\dpi{100} 243$

$\dpi{100} 729$

Explanation

A power raised to a power indicates that you multiply the two powers.

$\dpi{100} (3^{3})^{2}=3^{3\cdot 2}=3^{6}$

What is the slope of the line that passes through the points and ?

Explanation

The slope of a line is sometimes referred to as "rise over run." This is because the formula for slope is the change in y-value (rise) divided by the change in x-value (run). Therefore, if you are given two points, $(x_{1},y_{1})$ and $(x_{2},y_{2})$ , the slope of their line can be found using the following formula: $slope=(y_{1}-y_{2})/(x_{1}-x_{2})$

This gives us .

What is the slope of the line that passes through the points and ?

Explanation

This gives us .

Solve:

$5^{-19}\times5^{17}$

$\frac{1}{25}$

$-\frac{1}{27}$

Explanation

In order to solve this problem, we need to recall our exponent rules:

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem

$5^{-19}\times 5^{17}=5^{(-19+17)}$

Solve for the exponents

$5^{-2}$

We cannot leave this problem in this format because we cannot have a negative exponent. Instead, we can move the base and the exponent to the denominator of a fraction:

$a^{(-m)}=\frac{1}{a^m}$

Solve the problem

$\frac{1}{5^{2}}=\frac{1}{25}$

Solve:

$5^{-19}\times5^{17}$

$\frac{1}{25}$

$-\frac{1}{27}$

Explanation

In order to solve this problem, we need to recall our exponent rules:

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem

$5^{-19}\times 5^{17}=5^{(-19+17)}$

Solve for the exponents

$5^{-2}$

We cannot leave this problem in this format because we cannot have a negative exponent. Instead, we can move the base and the exponent to the denominator of a fraction:

$a^{(-m)}=\frac{1}{a^m}$

Solve the problem

$\frac{1}{5^{2}}=\frac{1}{25}$

What is the slope of the line with the equation