Skip to main content

Exponents (Exponents of Exponents)

Sometimes when working with exponents, you'll see exponents raised to another number, such as: $(x^2)^5$

The rules of exponents still apply.  The exponent of 5, means that you want to raise the base $(x^2)$ to the power of 5. In other words, multiply $(x^2)$ times itself 5 times.

$$\eqalign{\text{}&(x^2)^5&&=(x^2)(x^2)(x^2)(x^2)(x^2)\\\text{You can write it out even further     }&(x^2)^5&&=(x\times x)(x\times x)(x\times x)(x\times x)(x\times x)\\\text{Or, even further...} &(x^2)^5&&=x\times x \times x \times x \times x \times x\times x \times x \times x\times x\\\text{Then count up your bases and simplify     }&(x^2)^5&&=x^{10}}$$

Do you see the trick?  When you raise an exponent to another exponent, you just have to multiply the two exponents together and raise the base to that exponent.  But, if you forget the trick you can always write it out and count on the bases.

Practice Problems:

  • Exponents (Exponents of Exponents)

    Find the exponents of exponents below (you can leave your final answer in exponential form):


    1. $(x^3)^4$=

    2. $(t^4)^2$=

    3. $(p^{12})^4$=

    4. $(8y)^3$=

    5. $[(-10g)^2]^3$=

    6. $(a^m)^n$=

    7. $(3k^4)^4$=

    8. $(-2w^3)^5$=

    9. $[(-0.3)^5]^2$=

    10. $(4a^3)^2$=

    11. $(x^2)^0$=

    12. $(5z)^3$=