Rules of Exponents Flashcard:

Front

What is the exponential form of \( (-\frac{2}{3})^5 \)?

Back

\((-\frac{2}{3})^5 = (-\frac{2}{3}) \times (-\frac{2}{3}) \times (-\frac{2}{3}) \times (-\frac{2}{3}) \times (-\frac{2}{3})\)

Front

What is the product of \( x^{20} \) and \( x^{10} \)?

Back

\( x^{20} \cdot x^{10} = x^{30} \)

Front

What is \( (4^{-2})^3 \) simplified?

Back

\( (4^{-2})^3 = \frac{1}{4^6} \)

Front

Simplify \( (2^4)(2^5) \).

Back

\( (2^4)(2^5) = 2^{4+5} = 2^9 \)

Front

What is the rule for multiplying powers with the same base?

Back

When multiplying powers with the same base, add the exponents: \( a^m \cdot a^n = a^{m+n} \)

Front

What is the rule for dividing powers with the same base?

Back

When dividing powers with the same base, subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \)

Front

What is the power of a power rule?

Back

When raising a power to another power, multiply the exponents: \( (a^m)^n = a^{m \cdot n} \)

Front

What is the value of \( 2^0 \)?

Back

Any non-zero number raised to the power of zero is 1: \( 2^0 = 1 \)

Front

What is the value of \( (-3)^2 \)?

Back

\( (-3)^2 = 9 \) because the negative sign is squared.

Front

What is the value of \( (-2)^3 \)?

Back

\( (-2)^3 = -8 \) because the negative sign is cubed.