Negative Integer Exponents

Front

What is the definition of a negative integer exponent?

Back

A negative integer exponent indicates that the base should be taken as the reciprocal raised to the absolute value of the exponent. For example, a^{-n} = 1/a^n.

Front

How can you express 7^{-3} using positive exponents?

Back

7^{-3} can be expressed as \frac{1}{7^3}.

Front

What is the result of y^{-1} in terms of positive exponents?

Back

y^{-1} can be expressed as \frac{1}{y}.

Front

How do you simplify the expression \frac{8^{-2}}{5}?

Back

\frac{8^{-2}}{5} simplifies to \frac{1}{5 \cdot 8 \cdot 8}.

Front

Identify the expression that is different from the others: \frac{1}{8}, \frac{1}{2^3}, \frac{1}{4}, \frac{1}{8^1}.

Back

\frac{1}{8} is different because it is not expressed in terms of a power of 2.

Front

What is the equivalent expression for \frac{1}{z^{-3}}?

Back

\frac{1}{z^{-3}} can be expressed as z^3.

Front

What is the general rule for converting negative exponents to positive exponents?

Back

The general rule is that a^{-n} = \frac{1}{a^n}.

Front

How do you handle negative exponents in a fraction?

Back

When dealing with negative exponents in a fraction, apply the rule of reciprocals to convert them to positive exponents.

Front

What is the value of 2^{-3} and how is it calculated?

Back

2^{-3} = \frac{1}{2^3} = \frac{1}{8}.

Front

If a = 3, what is the value of a^{-2}?

Back

If a = 3, then a^{-2} = \frac{1}{3^2} = \frac{1}{9}.