Evaluate the Expressions With Exponents Worksheets - Free Printable

To solve these problems, we need to evaluate each expression using the given value $y = 8$.

Important Note from the worksheet: The dot symbol ($\bullet$) means multiplication. Also, remember that exponents (powers) must be calculated before multiplying or adding (following the order of operations).

First, let's find the values for the powers of $y$:
* $y = 8$
* $y^2 = 8 \times 8 = 64$
* $y^3 = 8 \times 8 \times 8 = 512$

Now, we will substitute these values into each problem and solve step-by-step.

1. $8 \bullet y^3 + 3 \bullet y^2$
* Substitute: $8 \bullet 512 + 3 \bullet 64$
* Multiply: $4096 + 192$
* Add: $4288$

2. $3 \bullet y^2 + 9 \bullet y^2$
* *Shortcut:* You can combine like terms first: $(3 + 9)y^2 = 12y^2$.
* Substitute: $12 \bullet 64$
* Multiply: $768$

3. $3 \bullet y^2 + 3 \bullet y^3$
* Substitute: $3 \bullet 64 + 3 \bullet 512$
* Multiply: $192 + 1536$
* Add: $1728$

4. $5 \bullet y^2 + 3 \bullet y^2$
* *Shortcut:* Combine like terms: $(5 + 3)y^2 = 8y^2$.
* Substitute: $8 \bullet 64$
* Multiply: $512$

5. $8 \bullet y^2 + 10 \bullet y^2$
* *Shortcut:* Combine like terms: $(8 + 10)y^2 = 18y^2$.
* Substitute: $18 \bullet 64$
* Multiply: $1152$

6. $6 \bullet y^2 + 3 \bullet y^2$
* *Shortcut:* Combine like terms: $(6 + 3)y^2 = 9y^2$.
* Substitute: $9 \bullet 64$
* Multiply: $576$

7. $5 \bullet y^2 + 5 \bullet y^2$
* *Shortcut:* Combine like terms: $(5 + 5)y^2 = 10y^2$.
* Substitute: $10 \bullet 64$
* Multiply: $640$

8. $7 \bullet y^2 + 10 \bullet y^2$
* *Shortcut:* Combine like terms: $(7 + 10)y^2 = 17y^2$.
* Substitute: $17 \bullet 64$
* Multiply: $1088$

9. $5 \bullet y^2 + 4 \bullet y^2$
* *Shortcut:* Combine like terms: $(5 + 4)y^2 = 9y^2$.
* Substitute: $9 \bullet 64$
* Multiply: $576$

10. $2 \bullet y^2 + 5 \bullet y^2$
* *Shortcut:* Combine like terms: $(2 + 5)y^2 = 7y^2$.
* Substitute: $7 \bullet 64$
* Multiply: $448$

Final Answer:
1. 4288
2. 768
3. 1728
4. 512
5. 1152
6. 576
7. 640
8. 1088
9. 576
10. 448