Powers — Practice Quiz

A Algebra cheat sheet for Powers — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Product Rule

$$a^n \cdot a^m = a^{n+m}$$

Quotient Rule

$$\frac{a^n}{a^m} = a^{n-m}$$

Power of a Power

$$(a^n)^m = a^{nm}$$

Power of a Product

$$(ab)^n = a^n b^n$$

Power of a Quotient

$$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$

Negative Exponent

$$a^{-n} = \frac{1}{a^n}$$

Zero Exponent (\(a \neq 0\))

$$a^0 = 1$$

Practice quiz

  1. Simplify the expression $x^5 \cdot x^3$.

    • $x^8$
    • $x^{15}$
    • $x^2$
    • $2x^8$

    Answer: $x^8$

  2. Simplify the expression $\frac{y^7}{y^2}$.

    • $y^9$
    • $y^{14}$
    • $y^5$
    • $y^{-5}$

    Answer: $y^5$

  3. What is the simplified form of $(z^4)^3$?

    • $z^7$
    • $z^{12}$
    • $z^{64}$
    • $3z^4$

    Answer: $z^{12}$

  4. Expand $(2a^3)^4$.

    • $2a^{12}$
    • $8a^{12}$
    • $16a^{12}$
    • $16a^7$

    Answer: $16a^{12}$

  5. Simplify $(\frac{m^2}{n^3})^3$.

    • $\frac{m^5}{n^6}$
    • $\frac{m^6}{n^9}$
    • $\frac{m^6}{n^6}$
    • $\frac{m^2}{n^9}$

    Answer: $\frac{m^6}{n^9}$

  6. Express $5^{-2}$ as a fraction.

    • $-25$
    • $\frac{1}{25}$
    • $\frac{1}{10}$
    • $25$

    Answer: $\frac{1}{25}$

  7. Evaluate $(100x^2y^3)^0$, assuming $x \neq 0$ and $y \neq 0$.

    • $100$
    • $0$
    • $1$
    • $100x^2y^3$

    Answer: $1$

  8. Simplify $a^4 \cdot a^{-2}$.

    • $a^6$
    • $a^{-8}$
    • $a^2$
    • $\frac{1}{a^2}$

    Answer: $a^2$

  9. Simplify $\frac{b^3}{b^{-2}}$.

    • $b^1$
    • $b^5$
    • $b^{-6}$
    • $\frac{1}{b^5}$

    Answer: $b^5$

  10. Simplify $(x^{-3})^2$.

    • $x^{-1}$
    • $x^6$
    • $x^{-6}$
    • $\frac{1}{x^6}$

    Answer: $\frac{1}{x^6}$

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