To simplify expressions where you are dividing powers with the same base, you subtract the exponent in the denominator (bottom) from the exponent in the numerator (top).
The rule is: $\frac{a^m}{a^n} = a^{m-n}$
Let's solve each problem step by step:
1.
$\frac{4^6}{4^2}$
* Subtract exponents: $6 - 2 = 4$
* Result: $4^4$
* Calculate value: $4 \times 4 \times 4 \times 4 = 256$
2.
$\frac{4^8}{4^2}$
* Subtract exponents: $8 - 2 = 6$
* Result: $4^6$
* Calculate value: $4 \times 4 \times 4 \times 4 \times 4 \times 4 = 4096$
3.
$\frac{9^7}{9^6}$
* Subtract exponents: $7 - 6 = 1$
* Result: $9^1$
* Calculate value: $9$
4.
$\frac{8^6}{8^1}$
* Subtract exponents: $6 - 1 = 5$
* Result: $8^5$
* Calculate value: $8 \times 8 \times 8 \times 8 \times 8 = 32,768$
5.
$\frac{3^4}{3^4}$
* Subtract exponents: $4 - 4 = 0$
* Result: $3^0$
* Calculate value: Any non-zero number to the power of 0 is 1. So, $1$.
6.
$\frac{7^6}{7^1}$
* Subtract exponents: $6 - 1 = 5$
* Result: $7^5$
* Calculate value: $7 \times 7 \times 7 \times 7 \times 7 = 16,807$
7.
$\frac{7^2}{7^1}$
* Subtract exponents: $2 - 1 = 1$
* Result: $7^1$
* Calculate value: $7$
8.
$\frac{9^8}{9^4}$
* Subtract exponents: $8 - 4 = 4$
* Result: $9^4$
* Calculate value: $9 \times 9 \times 9 \times 9 = 6,561$
9.
$\frac{4^5}{4^4}$
* Subtract exponents: $5 - 4 = 1$
* Result: $4^1$
* Calculate value: $4$
10.
$\frac{8^3}{8^3}$
* Subtract exponents: $3 - 3 = 0$
* Result: $8^0$
* Calculate value: Any non-zero number to the power of 0 is 1. So, $1$.
Final Answer:
1. 256
2. 4096
3. 9
4. 32,768
5. 1
6. 16,807
7. 7
8. 6,561
9. 4
10. 1
Parent Tip: Review the logic above to help your child master the concept of rules for dividing exponents worksheet.
