Math ↠ Exponents and roots ↠ Exponent laws

Exponent laws

The exponent laws govern how exponentiations behave when you use multiplication, division or multiple exponentiation.

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Remember

These exponent laws do not apply to adding and subtracting.

    Same base

  1. $a^x\cdot a^y=a^{x+y}$
  2. $a^x : a^y=\frac{a^x}{a^y}=a^{x-y}$

    3. Same exponent

  3. $a^x\cdot b^x=(a\cdot b)^x$
  4. $a^x : b^x=\frac{a^x}{b^x}=(\frac{a}{b})^x$

    5. Multiple exponentiation

  5. $(a^x)^y=a^{x\cdot y}$

Examples

  • $3^2\cdot3^3=3^{2+3}=3^5$
  • $\frac{3^3}{3^2}=3^{3-2}=3$

  • $3^2\cdot4^2=(3\cdot4)^2=12^2$
  • $\frac{3^2}{4^2}=(\frac{3}{4})^2$

  • $(2^3)^2=2^{3\cdot2}=2^6$