Zero and Negative Exponents - Vaccarella

When a base is raised to the power of zero, such as 5⁰, the overall value of the expression is always...

• -1

• 0

• 1

• The value of the base

Answer explanation

When a number is raised to the power of zero, the value of the expression is 1.

Think of it as meaning we are multiplying by that base zero times, leaving us with the "invisible" 1.

Example:

$5^0$
$=1\cdot5^0$
$=1$
(multiplied by zero 5's)

Below is an expression with a negative exponent. Select the equivalent expression that has a positive exponent, instead.

  $\frac{1}{x^{-2}}$  

•  $\frac{1}{x^2}$  

•  $x^2$  

•  $\frac{1}{x^{-2}}$  

•  $x^{-2}$  

Answer explanation

To rewrite an exponent expression with a positive exponent, you must write the reciprocal of the term (switch to/from numerator and denominator) and change the sign of the exponent.

 $\frac{1}{x^{-2}}\ =\ x^2$  

Below is an expression with a negative exponent. Select the equivalent expression that has a positive exponent, instead.

  $2x^{-3}$  

•  $\frac{1}{2x^{-3}}$  

•  $2x^3$  

•  $\frac{1}{2x^3}$  

•  $\frac{2}{x^3}$  

•  $\frac{2}{x^{-3}}$  

Answer explanation

To rewrite an exponent expression with a positive exponent, you must write the reciprocal of the term and change the sign of the exponent.

When there is a coefficient, the coefficient remains where it was! Only the power portion of the term is affected.

 $2x^{-3\ \ }$  

  $=\ \ 2\cdot x^{-3}\$  

  $\ =\ \ 2\cdot\frac{1}{x^3}\ \$  

  $=\ \ \frac{2}{x^3}$  

Below is an expression with zero and negative exponents. Select the simplified equivalent expression:

  $x^0\cdot y^{-2}$  

•  $xy^2$  

•  $y^2$  

•  $\frac{1}{y^2}$  

•  $\frac{x}{y^2}$  

Answer explanation

ORDER OF OPERATIONS: Exponents, then multiplication

 $x^0\cdot y^{-2}$  

  $=1\cdot y^{-2}$  

  $=1\cdot\frac{1}{y^2}$  

  $=\frac{1}{y^2}$  

Any base to the 0 power is equal to....

• 0

• the base

• 1

• x

Simplify x^-7

• -7
• -7x
• 1/x⁷
• -1/x⁷

Make this negative exponent positive.
9^-3

• 9³
• 1/9^-3
• 1/9³
• 729

Simplify (-9)⁰

• -9
• -1
• 1
• 9

Which is greater,  2654⁰ or 5⁰?

• 2654⁰
• 5⁰
• They are the same
• Zero is greater

Rewrite using a positive exponent.
g^-7

• ¹/_g⁷
• g⁷
• ¹/_g^-7
• -g⁷