Let’s solve each problem step by step using the
Power Rule for exponents:
> When you have a power raised to another power, like $(a^m)^n$, you multiply the exponents:
> $(a^m)^n = a^{m \cdot n}$
Also, if there are multiple variables inside parentheses, like $(x^a y^b)^c$, you apply the outer exponent to *each* variable:
$(x^a y^b)^c = x^{a \cdot c} y^{b \cdot c}$
And remember: any nonzero number (or expression) raised to the 0 power is 1. So $anything^0 = 1$ (as long as it’s not zero itself).
---
Now let’s go one by one.
Left Column:
1. $(x^2)^2$ → Multiply exponents: $2 \cdot 2 = 4$ → $x^4$
2. $(x^2)^3$ → $2 \cdot 3 = 6$ → $x^6$
3. $(x^2)^6$ → $2 \cdot 6 = 12$ → $x^{12}$
4. $(y^3)^2$ → $3 \cdot 2 = 6$ → $y^6$
5. $(x^4)^0$ → Anything to the 0 power is 1 → $1$
---
Right Column:
6. $(x^2 y^2)^3$ → Apply exponent 3 to both:
$x^{2\cdot3} y^{2\cdot3} = x^6 y^6$
7. $(x^2 y^4)^5$ → $x^{2\cdot5} y^{4\cdot5} = x^{10} y^{20}$
8. $(x y^4)^3$ → Remember: $x$ is same as $x^1$
So: $x^{1\cdot3} y^{4\cdot3} = x^3 y^{12}$
9. $(x y^6)^4$ → $x^{1\cdot4} y^{6\cdot4} = x^4 y^{24}$
10. $(x^0)^5$ → First, $x^0 = 1$, then $1^5 = 1$
OR: multiply exponents: $0 \cdot 5 = 0$, so $x^0 = 1$ → Answer is still $1$
---
✔ All answers checked and verified.
Final Answer:
Left column:
$x^4$, $x^6$, $x^{12}$, $y^6$, $1$
Right column:
$x^6 y^6$, $x^{10} y^{20}$, $x^3 y^{12}$, $x^4 y^{24}$, $1$
Parent Tip: Review the logic above to help your child master the concept of powers and exponents worksheet pdf.
